On the character of certain irreducible modular representations
HTML articles powered by AMS MathViewer
- by G. Lusztig
- Represent. Theory 19 (2015), 3-8
- DOI: https://doi.org/10.1090/S1088-4165-2015-00463-7
- Published electronically: March 2, 2015
- PDF | Request permission
Abstract:
Let $G$ be an almost simple, simply connected algebraic group over an algebraically closed field of characteristic $p>0$. In this paper we restate our conjecture from 1979 on the characters of irreducible modular representations of $G$ so that it is now directly applicable to any dominant highest weight.References
- H. H. Andersen, J. C. Jantzen, and W. Soergel, Representations of quantum groups at a $p$th root of unity and of semisimple groups in characteristic $p$: independence of $p$, Astérisque 220 (1994), 321 (English, with English and French summaries). MR 1272539
- Peter Fiebig, An upper bound on the exceptional characteristics for Lusztig’s character formula, J. Reine Angew. Math. 673 (2012), 1–31. MR 2999126, DOI 10.1515/CRELLE.2011.170
- Jens Carsten Jantzen, Moduln mit einem höchsten Gewicht, Lecture Notes in Mathematics, vol. 750, Springer, Berlin, 1979 (German). MR 552943, DOI 10.1007/BFb0069521
- Shin-ichi Kato, On the Kazhdan-Lusztig polynomials for affine Weyl groups, Adv. in Math. 55 (1985), no. 2, 103–130. MR 772611, DOI 10.1016/0001-8708(85)90017-9
- David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184. MR 560412, DOI 10.1007/BF01390031
- George Lusztig, Some problems in the representation theory of finite Chevalley groups, The Santa Cruz Conference on Finite Groups (Univ. California, Santa Cruz, Calif., 1979) Proc. Sympos. Pure Math., vol. 37, Amer. Math. Soc., Providence, R.I., 1980, pp. 313–317. MR 604598
- G. Lusztig, Modular representations and quantum groups, Classical groups and related topics (Beijing, 1987) Contemp. Math., vol. 82, Amer. Math. Soc., Providence, RI, 1989, pp. 59–77. MR 982278, DOI 10.1090/conm/082/982278
- Robert Steinberg, Representations of algebraic groups, Nagoya Math. J. 22 (1963), 33–56. MR 155937, DOI 10.1017/S0027763000011016
- G.Williamson, Schubert calculus and torsion, arxiv:1309.5055.
Bibliographic Information
- G. Lusztig
- Affiliation: Department of Mathematics, M.I.T., Cambridge, Massachusetts 02139
- MR Author ID: 117100
- Email: gyuri@math.mit.edu
- Received by editor(s): October 7, 2014
- Received by editor(s) in revised form: February 2, 2015
- Published electronically: March 2, 2015
- Additional Notes: This work was supported in part by National Science Foundation grant DMS-1303060 and by a Simons Fellowship.
- © Copyright 2015 American Mathematical Society
- Journal: Represent. Theory 19 (2015), 3-8
- MSC (2010): Primary 20G99
- DOI: https://doi.org/10.1090/S1088-4165-2015-00463-7
- MathSciNet review: 3316914