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RATIONAL REPRESENTATIONS OF GL2

Published online by Cambridge University Press:  08 December 2010

VANESSA MIEMIETZ  and
WILL TURNER
VANESSA MIEMIETZ
Affiliation:
Mathematical Institute, University of Oxford, Oxford, England e-mail: miemietz@maths.ox.ac.uk
WILL TURNER
Affiliation:
Department of Mathematics, University of Aberdeen, Scotland e-mail: w.turner@abdn.ac.uk
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Abstract

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Let F be an algebraically closed field of characteristic p. We fashion an infinite dimensional basic algebra ←p(F), with a transparent combinatorial structure, which controls the rational representation theory of GL2(F).

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 2 , May 2011 , pp. 257 - 275
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Cline, E., Parshall, B. and Scott, L., Finite-dimensional algebras and highest weight categories, J. Reine Angew. Math. 391 (1988), 85–99. MR961165 (90d:18005).Google Scholar
2.Dlab, V., Quasi-hereditary algebras revisited, An. Ştiinţ. Univ. Ovidius Constanţa Ser. Mat. 4 (2) (1996), 43–54, Representation theory of groups, algebras and orders (Constanţa, 1995).Google Scholar
3.Donkin, S., in The q-Schur algebra, London Mathematical Society Lecture Note Series, vol. 253 (Cambridge University Press, Cambridge, UK, 1998). MR1707336 (2001h:20072).CrossRefGoogle Scholar
4.Erdmann, K. and Henke, A., On Ringel duality for Schur algebras, Math. Proc. Cambridge Philos. Soc. 132 (1) (2002), 97–116. MR1866327 (2002j:20081).Google Scholar
5.Green, J. A., Polynomial representations of GLn, Algebra, Carbondale 1980 (Proc. Conf., Southern Illinois Univ., Carbondale, Ill., 1980), lecture notes in Math., vol. 848 (Springer, Berlin, 1981), 124–140. MR613180 (82i:20019).Google Scholar
6.Henke, A., The Cartan matrix of the Schur algebra S(2, r), Archiv der Mathematik 76 (2001), 416–425. MR1831497 (2002b:20014).Google Scholar
7.Henke, A. and Koenig, S., Relating polynomial GL(n)-representations in different degrees, J. Reine Angew. Math. 551 (2002), 219–235. MR1932179 (2003k:20066).Google Scholar
8.Jantzen, J. C., in Representations of algebraic groups, 2nd edn., Mathematical Surveys and Monographs, vol. 107 (American Mathematical Society, Providence, RI, 2003). MR2015057 (2004h:20061).Google Scholar
9.Miemietz, V. and Turner, W., Homotopy, homology, and GL 2, Proc. London Math. Soc. 100(2) (2010), 585–606. arXiv:0809.0988[mathRT].Google Scholar
10.Parshall, B. and Scott, L., Derived categories, quasi-hereditary algebras, and algebraic groups (1988), http://www.math.virginia.edu/lls2l/reprnt.htmGoogle Scholar
11.Ringel, C. M., The category of modules with good filtrations over a quasi-hereditary algebra has almost split sequences, Math. Z. 208 (2) (1991), 209–223. MR1128706 (93c:16010).CrossRefGoogle Scholar
12.Turner, W., Rock blocks (2004), http://www.maths.ox.ac.uk/turnerw/Google Scholar
13.Turner, W., Tilting equivalences: from hereditary algebras to symmetric groups (2006), http://www.maths.ox.ac.uk/turnerw/Google Scholar