Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-13T07:17:58.821Z Has data issue: false hasContentIssue false

References

Published online by Cambridge University Press:  14 February 2020

François Digne
Affiliation:
Université de Picardie Jules Verne, Amiens
Jean Michel
Affiliation:
Centre National de la Recherche Scientifique (CNRS), Paris
Get access

Summary

Image of the first page of this content. For PDF version, please use the ‘Save PDF’ preceeding this image.'
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2020

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Adams, J., and He, X. 2017. Lifting of elements of Weyl groups. J. Algebra, 485, 142–165.Google Scholar
Alvis, D. 1980. Duality in the character ring of a finite Chevalley group. In The Santa Cruz Conference on Finite Groups. Proc. Symp. in Pure Math., vol. 37, 353–357, University of California, Santa Cruz, CA.Google Scholar
Alvis, D., Lusztig, G., and Spaltenstein, N. 1982. On Springer's correspondence for simple groups of type En(n = 6,7,8). Math. Proc. Camb. Phil. Soc., 92, 65–78.Google Scholar
Benson, C. T., and Curtis, C. W. 1972. On the degrees and rationality of certain characters of finite Chevalley groups. Trans. Amer. Math. Soc., 165, 251–273.Google Scholar
Beynon, W. M., and Spaltenstein, N. 1984. Green functions of finite Chevalley groups of type En(n = 6,7,8). J. Algebra, 88, 584–614.Google Scholar
Bonnafé, C. 2005a. Actions of relative Weyl groups II. J. Group Theory, 8, 351–387.CrossRefGoogle Scholar
Bonnafé, C. 2005b. Quasi-isolated elements in reductive groups. Comm. Algebra, 33, 2315–2337.Google Scholar
Bonnafé, C. 2006. Sur les caractères des groupes réductifs finis à centre non connexe: applications aux groupes spéciaux linéaires et unitaires. Astérisque, 306, 1–174.Google Scholar
Bonnafé, C. 2010. Representations of SL2(Fq). London, Springer Verlag.Google Scholar
Bonnafé, C., and Michel, J. 2011. A computational proof of the Mackey formula for q > 2. J. Algebra, 327, 506–526.Google Scholar
Bonnafé, C., and Rouquier, R. 2006. On the irreducibility of Deligne–Lusztig varieties. C. R. Math. Acad. Sci. Paris, 343, 37–39.Google Scholar
Borel, A. 1991. Linear Algebraic Groups. Second enlarged ed. Graduate Texts in Mathematics, no. 126. New York, Springer Verlag.Google Scholar
Borel, A., and Tits, J. 1965. Groupes réductifs. Publ. Math. Inst. Hautes Études Sci., 27, 55–160.Google Scholar
Borel, A., Carter, R., Curtis, C. W., Iwahori, N., Springer, T. A., and Steinberg, R. 1970. Seminar on Algebraic Groups and Related Topics. Lecture Notes in Mathematics, no. 131. New York, Springer Verlag.Google Scholar
Borho, W., and MacPherson, R. 1981. Représentations des groupes de Weyl et homologie d'intersection pour les variétés nilpotentes. C. R. Math. Acad. Sci. Paris, 292, 707–710.Google Scholar
Bourbaki, N. 1968. Groupes et algèebres de Lie, chapters IV, V, VI. Hermann, Paris.Google Scholar
Bourbaki, N. 1971. Algèebre, chapters 1–3. Hermann/Addison-Wesley, Paris.Google Scholar
Bourbaki, N. 1975. Algèebre commutative, chapters 5–7. Springer Verlag, Berlin.Google Scholar
Bourbaki, N. 1981. Algèebre, chapter 8. Springer Verlag, Berlin.Google Scholar
Broué, M. 2017. On Characters of Finite Groups. Mathematical Lectures from Peking University. Springer Verlag.Google Scholar
Broué, M., Malle, G., and Michel, J. 1999. Towards Spetses I. Transformation Groups, 4, 157–218.Google Scholar
Carter, R. W. 1985. Finite Groups of Lie Type: Conjugacy Classes and Complex Characters. Chichester, Wiley-Interscience.Google Scholar
Chevalley, C. 1955. Invariants of finite reflection groups. Amer. J. Math., 77, 778–782.CrossRefGoogle Scholar
Chevalley, C. 1994. Sur les décompositions cellulaires des espaces G/B. In Algebraic Groups and Their Generalizations: Classical Methods (University Park, PA, 1991). Proc. Symp. Pure Math., vol. 56, 1–23. American Mathematical Society, Providence, RI.Google Scholar
Chevalley, C. 2005. Classification des groupes algébriques semi-simples. Collected works, vol. 3. Springer Verlag, Berlin.Google Scholar
Curtis, C. W. 1980. Truncation and duality in the character ring of a finite group of Lie type. J. Algebra, 62, 320–332.Google Scholar
Curtis, C. W., and Reiner, I. 1981. Methods of Representation Theory I. Wiley-Interscience, New York.Google Scholar
Deligne, P. 1977. Cohomologie étale. Lecture Notes in Mathematics, no. 569. Springer Verlag. Séminaire de Géométrie Algébrique du Bois-Marie SGA 4 1/2, Avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier.Google Scholar
Deligne, P. 1980. La conjecture de Weil II. Publ. Math. Inst. Hautes Études Sci., 43, 137–252.Google Scholar
Deligne, P., and Lusztig, G. 1976. Representations of reductive groups over finite fields. Ann. of Math., 103, 103–161.Google Scholar
Deligne, P., and Lusztig, G. 1982. Duality for representations of a reductive group over a finite field. J. Algebra, 74, 284–291.Google Scholar
Deligne, P., and Lusztig, G. 1983. Duality for representations of a reductive group over a finite field II. J. Algebra, 81, 540–545.CrossRefGoogle Scholar
Deodhar, V. 1989. A note on subgroups generated by reflections in Coxeter groups. Arch. Math., 53, 543–546.Google Scholar
Deriziotis, D. I. 1984. Conjugacy classes and centralizers of semi-simple elements in finite groups of Lie type. Vorlesungen aus dem Fachbereich Mathematik der Universität Essen, 11.Google Scholar
Digne, F., and Michel, J. 1982. Remarques sur la dualité de Curtis. J. Algebra, 79, 151–160.Google Scholar
Digne, F., and Michel, J. 1983. Foncteur de Lusztig et fonctions de Green généralisées. C. R. Math. Acad. Sci. Paris, 297, 89–92.Google Scholar
Digne, F., and Michel, J. 1987. Foncteurs de Lusztig et caractèeres des groupes linéaires et unitaires sur un corps fini. J. Algebra, 107, 217–255.Google Scholar
Digne, F., and Michel, J. 1990. On Lusztig's parametrization of characters of finite groups of Lie type. Asterisque, 181–182, 113–156.Google Scholar
Digne, F., and Michel, J. 1994. Groupes réductifs non connexes. Ann. ENS, 27, 345–406.Google Scholar
Digne, F., Lehrer, G. I., and Michel, J. 1992. The characters of the group of rational points of a reductive group with non-connected centre. J. Reine Angew. Math., 425, 155–192.Google Scholar
Digne, F., Lehrer, G. I., and Michel, J. 1997. On Gelfand–Graev characters of reductive groups with disconnected centre. J. Reine Angew. Math., 491, 131–147.Google Scholar
Digne, F., Michel, J., and Rouquier, R. 2007. Cohomologie des variétés de Deligne–Lusztig. Adv. Math., 209, 749–822.Google Scholar
Dipper, R., and Du, J. 1993. Harish-Chandra vertices. J. Reine Angew. Math., 437, 101–130.Google Scholar
Dyer, M. 1990. Reflection subgroups of Coxeter systems. J. Algebra, 135, 57–73.Google Scholar
Geck, M. 1993. A note on Harish-Chandra induction. Manuscripta Math., 80, 393–401.Google Scholar
Geck, M. 1996. On the average value of the irreducible characters of finite groups of Lie type on geometric unipotent classes. Doc. Math. J. DMV, 1, 293–317.Google Scholar
Geck, M. 2003. An Introduction to Algebraic Geometry and Algebraic Groups. Oxford Graduate Texts in Mathematics, Vol. 10. Oxford University Press, Oxford.Google Scholar
Geck, M. 2019. Computing Green Functions in Small Characteristic. Arxiv: 1904.06970 [math.RT].Google Scholar
Geck, M., and Jacon, N. 2011. Representations of Hecke Algebras at Roots of Unity. Algebra and Applications, No. 15. Springer Verlag, London.Google Scholar
Geck, M., and Malle, G. 1999. On the existence of a unipotent support for the irreducible characters of a finite group of Lie type. Trans. Amer. Math. Soc., 352, 429–456.Google Scholar
Geck, M., and Malle, G. 2003. Fourier transforms and Frobenius eigenvalues for finite Coxeter groups. J. Algebra, 260, 162–193.Google Scholar
Geck, M., and Pfeiffer, G. 2000. Characters of Finite Coxeter Groups and Iwahori–Hecke Algebras. London Mathematical Society Monographs, Vol. 21. Oxford University Press, New York.Google Scholar
Geck, M., Hiss, G., Lubeck, F., Malle, G., and Pfeiffer, G. 1996a. CHEVIE A system for computing and processing generic character tables for finite groups of Lie type. Appl. Algebra Eng. Comm. Comput., 7, 175–210.Google Scholar
Geck, M., Hiss, G., and Malle, G. 1996b. Towards a classification of the irreducible representations in non-describing characteristic of a finite group of Lie type. Math. Z., 221(3), 353–386.Google Scholar
Gelfand, I. M., and Graev, M. I. 1962. Construction of irreducible representations of simple algebraic groups over a finite field. Doklady Akad. Nauk SSSR, 147, 529–532.Google Scholar
Gorenstein, D. 1980. Finite Groups. Chelsea Publishing, New York.Google Scholar
Green, J. 1955. The characters of the finite general linear groups. Trans. Amer. Math. Soc., 80, 402–447.Google Scholar
Grothendieck, A. 1967. éléments de géométrie algébrique IV. étude locale des schemas et des morphismes de schémas, quatrièeme partie. Publ. Math. Inst. Hautes Études Sci., 32, 5–361.Google Scholar
Grothendieck, A., et al. 1972–1973. Théorie des topos et cohomologie étale des schéma. Lecture Notes in Mathematics, Nos. 269, 270, 305. Springer Verlag, Berlin. Séminaire de Géométrie Algébrique du Bois-Marie 1963–1964 (SGA 4), Dirigé par M. Artin, A. Grothendieck et J. L. Verdier. Avec la collaboration de P. Deligne et B. Saint-Donat.Google Scholar
Grothendieck, A., et al. 1977. SGA 5. Cohomologie l-adique et fonctions L. Lecture Notes in Mathematics, No. 589. Springer Verlag, Berlin. Editor L. Illusie.Google Scholar
Harish-Chandra. 1970. Eisenstein series over finite fields. Pages 76–88 of: Functional Analysis and Related Fields. Springer Verlag, Berlin.Google Scholar
Hartshorne, R. 1977. Algebraic Geometry. Graduate Texts in Mathematics, No. 52. Springer Verlag, New York.Google Scholar
Hiller, H. 1982. Geometry of Coxeter groups. Pitman, Boston.Google Scholar
Howlett, R. B. 1974. On the degrees of Steinberg characters of Chevalley groups. Math. Z., 135, 125–135.CrossRefGoogle Scholar
Howlett, R. B., and Lehrer, G. I. 1980. Induced cuspidal representations and generalized Hecke rings. Invent. Math., 58, 37–64.Google Scholar
Howlett, R. B., and Lehrer, G. I. 1994. On Harish-Chandra induction and restriction for modules of Levi subgroups. J. Algebra, 165, 172–183.Google Scholar
Humphreys, J. E. 1975. Linear Algebraic Groups. Graduate Texts in Mathematics, No. 21. Springer Verlag, Berlin.Google Scholar
Kawanaka, N. 1982. Fourier transforms of nilpotently supported invariant functions on a simple Lie algebra over a finite field. Invent. Math., 69, 411–435.Google Scholar
Kazhdan, D. 1977. Proof of Springer's hypothesis. Israel J. Math., 28, 272–286.Google Scholar
Lang, S. 2002. Algebra. Revised 3rd ed. Graduate Texts in Mathematics, No. 211. Springer Verlag, New York.Google Scholar
Lehrer, G. I. 1978. On the characters of semisimple groups over finite fields. Osaka J. Math., 15, 77–99.Google Scholar
Liebeck, M., and Seitz, G. 2012. Unipotent and Nilpotent Classes in Simple Algebraic Groups and Lie Algebras. Mathematical Surveys and Monographs, Vol. 180. American Mathematical Society, Providence, RI.CrossRefGoogle Scholar
Lou, B. 1968. The centralizer of a regular unipotent element in a semi-simple algebraic group. Bull. Amer. Math. Soc., 74, 1144–1146.CrossRefGoogle Scholar
Lusztig, G. 1976a. Coxeter orbits and eigenspaces of Frobenius. Invent. Math., 28, 101–159.Google Scholar
Lusztig, G. 1976b. On the finiteness of the number of unipotent classes. Invent. Math., 34, 201–213.Google Scholar
Lusztig, G. 1977. Representations of finite classical groups. Invent. Math., 43, 125–175.Google Scholar
Lusztig, G. 1978. Representations of Finite Chevalley Groups. CBMS Regional Conference Series in Mathematics, Vol. 39. American Mathematical Society, Providence, RI. Expository lectures from the CBMS Regional Conference held at Madison, WI, August 8–12, 1977.Google Scholar
Lusztig, G. 1984a. Characters of Reductive Groups Over a Finite Field. Annals of Mathematics Studies, No. 107. Princeton University Press, Princeton, NJ.Google Scholar
Lusztig, G. 1984b. Intersection cohomology complexes on a reductive group. Invent. Math., 75, 205–272.Google Scholar
Lusztig, G. 1986a. Character sheaves IV. Advances in Math., 59, 1–63.Google Scholar
Lusztig, G. 1986b. Character sheaves V. Advances in Math., 61, 103–165.Google Scholar
Lusztig, G. 1986c. On the character values of finite Chevalley groups at unipotent elements. J. Algebra, 104, 146–194.Google Scholar
Lusztig, G. 1988. On the representations of reductive groups with disconnected center. Astérisque, 168, 157–166.Google Scholar
Lusztig, G. 1990. Green functions and character sheaves. Ann. Math., 131, 355–408.Google Scholar
Lusztig, G. 1992. A unipotent support for irreducible representations. Adv. Math., 94, 139–179.Google Scholar
Lusztig, G., and Spaltenstein, N. 1985. On the generalized Springer correspondence for classical groups. Pages 289–316 of: Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983). Adv. Stud. Pure Math., Vol. 6. North-Holland, Amsterdam.Google Scholar
Lusztig, G., and Srinivasan, B. 1977. The characters of the finite unitary groups. J. Algebra, 49, 167–171.Google Scholar
Malle, G. 1990. Die unipotenten Charaktere von 2F4(q2). Comm. Algebra, 18, 2361–2381.Google Scholar
Malle, G. 1999. On the rationality and fake degrees of characters of cyclotomic algebras. J. Math. Sci. Univ. Tokyo, 6, 647–677.Google Scholar
Malle, G., and Testerman, D. 2011. Linear Algebraic Groups and Finite Groups of Lie Type. Cambridge Studies in Advanced Mathematics, Vol. 133. Cambridge University Press, Cambridge.Google Scholar
Milne, J. S. 1980. étale cohomology. Princeton Mathematical Series, No. 33. Princeton University Press, Princeton, NJ.Google Scholar
Milne, J. S. 2017. Algebraic Groups. Cambridge Studies in Advanced Mathematics, No. 170. Cambridge University Press, Cambridge.Google Scholar
Mizuno, K. 1980. The conjugate classes of unipotent elements of the Chevalley groups E7 and E8. Tokyo J. Math., 3, 391–459.Google Scholar
Serre, J.-P. 1994. Cohomologie Galoisienne, 5th ed. Lecture Notes in Mathematics, No. 5. Springer Verlag, Berlin.Google Scholar
Shephard, G. C., and Todd, J. A. 1954. Finite unitary reflection groups. Canad. J. Math., 6, 274–304.Google Scholar
Shoji, T. 1979. On the Springer representations of the Weyl groups of classical algebraic groups. Comm. Algebra, 7, 1713–1745, 2027–2033.Google Scholar
Shoji, T. 1982. On the Green polynomials of a Chevalley group of type F4. Comm. Algebra, 10, 505–543.Google Scholar
Shoji, T. 1983. On the Green polynomials of classical groups. Invent. Math., 74, 239–267.Google Scholar
Shoji, T. 1987. Green functions of reductive groups over a finite field. Pages 289–301 of: The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986). Proc. Sympos. Pure Math., vol. 47. American Mathematical Society, Providence, RI.Google Scholar
Shoji, T. 1995. Character sheaves and almost characters of reductive groups I, II. Adv. Math., 111, 244–354.Google Scholar
Shoji, T. 2007. Generalized Green functions and unipotent classes for finite reductive groups, II. Nagoya Math. J., 188, 133–170.Google Scholar
Slodowy, P. 1980. Simple Singularities and Simple Algebraic Groups. Lecture Notes in Mathematics, No. 815. Springer Verlag, Berlin.Google Scholar
Spaltenstein, N. 1977. On the fixed point set of a unipotent element on the variety of Borel subgroups. Topology, 16, 203–204.Google Scholar
Spaltenstein, N. 1982. Classes unipotentes et sous-groupes de Borel. Lecture Notes in Mathematics, No. 946. Springer Verlag, Berlin.Google Scholar
Spaltenstein, N. 1985. On the generalized Springer correspondence for exceptional groups. Pages 317–338 of: Algebraic Groups and Related Topics (Kyoto/Nagoya, 1983). Adv. Stud. Pure Math., vol. 6. North-Holland, Amsterdam.Google Scholar
Springer, T. A. 1966a. A note on centralizers in semi-simple groups. Indag. Math., 28, 75–77.Google Scholar
Springer, T. A. 1966b. Some arithmetic results on semi-simple Lie algebras. Publ. Math. Inst. Hautes Études Sci., 30, 115–141.Google Scholar
Springer, T. A. 1974. Regular elements of finite reflection groups. Invent. Math., 25, 159–198.Google Scholar
Springer, T. A. 1976. Trigonometric sums, Green functions of finite groups and representations of Weyl groups. Invent. Math., 36, 173–207.Google Scholar
Springer, T. A. 1998. Linear Algebraic Groups, 2nd ed. Progress in Mathematics, No. 9. Birkhäuser, Boston.Google Scholar
Srinivasan, B. 1979. Representations of Finite Chevalley Groups. Lecture Notes in Mathematics, No. 764. Springer Verlag, Berlin.Google Scholar
Steinberg, R. 1956. Prime power representations of finite linear groups I. Canad. J. Math., 8, 580–591.Google Scholar
Steinberg, R. 1957. Prime power representations of finite linear groups II. Canad. J. Math., 9, 347–351.Google Scholar
Steinberg, R. 1968. Endomorphisms of linear algebraic groups. Mem. Am. Math. Soc., 80.Google Scholar
Steinberg, R. 1974. Conjugacy Classes in Algebraic Groups. Lecture Notes in Mathematics, No. 366. Springer Verlag, Berlin.Google Scholar
Steinberg, R. 2016. Lectures on Chevalley Groups. University Lecture Series, No. 66. American Mathematical Society, Providence, RI. Revised and corrected edition of the 1968 original.Google Scholar
Taylor, J. 2018. On the Mackey formula for connected centre groups. J. Group Theory, 21, 439–448.Google Scholar
Tits, J. 1964. Algebraic simple groups and abstract groups. Ann. Math., 80, 313–329.Google Scholar
Tits, J. 1966. Normalisateurs de tores. I. Groupes de Coxeter étendus. J. Algebra, 4, 96–116.Google Scholar
Zhelevinski, A. 1981. Representations of Finite Classical Groups. Lecture Notes in Mathematics, No. 869. Springer Verlag, Berlin.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • References
  • François Digne, Université de Picardie Jules Verne, Amiens, Jean Michel, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book: Representations of Finite Groups of Lie Type
  • Online publication: 14 February 2020
  • Chapter DOI: https://doi.org/10.1017/9781108673655.017
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • References
  • François Digne, Université de Picardie Jules Verne, Amiens, Jean Michel, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book: Representations of Finite Groups of Lie Type
  • Online publication: 14 February 2020
  • Chapter DOI: https://doi.org/10.1017/9781108673655.017
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • References
  • François Digne, Université de Picardie Jules Verne, Amiens, Jean Michel, Centre National de la Recherche Scientifique (CNRS), Paris
  • Book: Representations of Finite Groups of Lie Type
  • Online publication: 14 February 2020
  • Chapter DOI: https://doi.org/10.1017/9781108673655.017
Available formats
×