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Module structure of cells in unequal-parameter Hecke algebras

Published online by Cambridge University Press:  11 January 2016

Thomas Pietraho
Thomas Pietraho*
Affiliation:
Department of Mathematics, Bowdoin College, Brunswick, Maine 04011, USAtpietrah@bowdoin.edu
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Abstract

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A conjecture of Bonnafé, Geck, Iancu, and Lam parametrizes Kazhdan-Lusztig left cells for unequal-parameter Hecke algebras in type Bn by families of standard domino tableaux of arbitrary rank. Relying on a family of properties outlined by Lusztig and the recent work of Bonnafé, we verify the conjecture and describe the structure of each cell as a module for the underlying Weyl group.

Keywords

20C0805E10
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 198 , June 2010 , pp. 23 - 45
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2010

References

[1] Alvis, D., The left cells of the Coxeter group of type H4 , J. Algebra 107 (1987), 160–168.Google Scholar
[2] Bonnafé, C., On Kazhdan-Lusztig cells in type B, preprint, arXiv:0806.0214v2 [math.RT] Google Scholar
[3] Bonnafé, C., Geck, M., Iancu, L., and Lam, T., On domino insertion and Kazhdan-Lusztig cells in type Bn , to appear in Progr. Math., preprint.Google Scholar
[4] Bonnafé, C. and Iancu, L., Left cells in type Bn with unequal parameters, Represent. Theory 7 (2003), 587–609.CrossRefGoogle Scholar
[5] DuCloux, F., Positivity results for the Hecke algebras of noncrystallographic finite Coxeter group, J. Algebra 303 (2006), 731–741.Google Scholar
[6] Garfinkle, D., On the classification of primitive ideals for complex classical Lie algebras (I), Compos. Math. 75 (1990), 135–169.Google Scholar
[7] Garfinkle, D., On the classification of primitive ideals for complex classical Lie algebras (II), Compos. Math. 81 (1992), 307–336.Google Scholar
[8] Garfinkle, D., On the classification of primitive ideals for complex classical Lie algebras (III), Compos. Math. 88 (1993), 187–234.Google Scholar
[9] Geck, M., Constructible characters, leading coefficients and left cells for finite Coxeter groups with unequal parameters, Represent. Theory 6 (2002), 1–30.Google Scholar
[10] Geck, M., Left cells and constructible representations, Represent. Theory 9 (2005), 385–416.Google Scholar
[11] Geck, M., Kazhdan-Lusztig cells and the Murphy basis, Proc. Lond. Math. Soc. 93 (2006), 635–665.Google Scholar
[12] Geck, M., Relative Kazhdan-Lusztig cells, Represent. Theory 10 (2006), 481–524.Google Scholar
[13] Geck, M., On Iwahori-Hecke algebras with unequal parameters and Lusztig’s isomorphism theorem, to appear in Pure Appl. Math. Q., preprint. Google Scholar
[14] Geck, M. and Iancu, L., Lusztig’s a-function in type Bn in the asymptotic case, Nagoya Math. J. 182 (2006), 199–240.Google Scholar
[15] Geck, M. and Pfeiffer, G., Characters of Finite Coxeter Groups and Iwahori-Hecke Algebras, Lond. Math. Soc. Monogr. N.S. 21, Oxford University Press, New York, 2000.Google Scholar
[16] James, G. and Kerber, A., The Representation Theory of the Symmetric Group, Encyclopedia Math. Appl. 16, Addison-Wesley, Reading, MA, 1981.Google Scholar
[17] Kazhdan, D.A. and Lusztig, G., Schubert varieties and Poincaré duality, Proc. Sym-pos. Pure Math. 34 (1980), 185–203.CrossRefGoogle Scholar
[18] Lusztig, G., A class of irreducible representations of a Weyl group II, Indag. Math. 44 (1982), 219–226.CrossRefGoogle Scholar
[19] Lusztig, G., Characters of Reductive Groups over a Finite Field, Ann. of Math. Stud. 207, Princeton University Press, Princeton, 1984.Google Scholar
[20] Lusztig, G., “Left cells in Weyl groups,” in Lie Group Representations, Lecture Notes in Math. 1024, Springer, Berlin, 1983, 99–111.Google Scholar
[21] Lusztig, G., Hecke Algebras with Unequal Parameters, CRM Monogr. Ser. 18, Am. Math. Soc., Providence, 2003.Google Scholar
[22] McGovern, W. M., Left cells and domino tableaux in classical Weyl groups, Compos. Math. 101 (1996), 77–98; see also Errata, Compos. Math. 117 (1999), 117–121.Google Scholar
[23] Pietraho, T., Cells and constructible representations in type Bn , New York J. Math. 14 (2008), 411–430.Google Scholar
[24] Pietraho, T., Equivalence classes in the Weyl groups of type Bn , J. Algebraic Combin. 27 (2008), 247–262.Google Scholar
[25] Pietraho, T., A relation for domino Robinson-Schensted algorithms, Ann. Comb., 13 (2010), 519–532.Google Scholar
[26] Springer, T. A., Quelques applications de la cohomologie d’intersection, Sémin. Bour-baki 589 (1982), 249–273.Google Scholar
[27] van Leeuwen, M. A. A., The Robinson-Schensted and Schutzenberger algorithms, an elementary approach, Electron. J. Combin. 3 (1996).Google Scholar