Electronic Only Electronic Research Announcements
Representation Theory
ISSN 1088-4165
     

Kazhdan-Lusztig polynomials and a combinatoric for tilting modules

Author(s): Wolfgang Soergel
Journal: Represent. Theory 1 (1997), 83-114.
MSC (1991): Primary 05E99, 17B37
Posted: May 5, 1997
Original article: Represent. Theory 1 (1997)
Retrieve article in: PDF DVI PostScript
This article is available free of charge

Abstract | References | Similar articles | Additional information

Abstract: This article gives a self-contained treatment of the theory of
Kazhdan-Lusztig polynomials with special emphasis on affine reflection groups. There are only a few new results but several new proofs. We close with a conjectural character formula for tilting modules, which formed the starting point of these investigations.


References:

[AJS94]
Henning Haahr Andersen, Jens Carsten Jantzen, and Wolfgang 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), 1-320.MR 95j:20036

[And86]
Henning Haahr Andersen, An inversion formula for the Kazhdan-Lusztig polynomials for affine Weyl groups, Advances in Mathematics 60 (1986), 125-153.MR 87j:22025

[And92]
Henning Haahr Andersen, Tensor products of quantized tilting modules, Comm. Math. Physics 149 (1992), 149-159.MR 94b:17015

[And96]
Henning Haahr Andersen, Filtrations and tilting modules, Aarhus Preprint No 7, 1996.

[BGS96]
Alexander A. Beilinson, Victor Ginzburg, and Wolfgang Soergel, Koszul duality patterns in representation theory, J. Amer. Math. Soc. 9 (1996), no. 2, 473-527.MR 96k:17010

[Bou81]
Nicolas Bourbaki, Groupes et algèbres de Lie, vol. 4-6, Masson, 1981.MR 83g:17001

[Deo87]
Vinay V. Deodhar, On some geometric aspects of Bruhat orderings II. The parabolic analogue of Kazhdan-Lusztig polynomials, Journal of Algebra 111 (1987), 483-506.MR 89a:20054

[Deo91]
Vinay V. Deodhar, Duality in parabolic set up for questions in Kazhdan-Lusztig theory, Journal of Algebra 142 (1991), 201-209.MR 92j:20049

[Deo94]
Vinay V. Deodhar, A brief survey of Kazhdan-Lusztig theory and related topics, Proceedings of Symposia in Pure Mathematics 56, Part 1, AMS, 1994, pp. 105-124.MR 96d:20039

[Don93]
Stephen Donkin, On tilting modules for algebraic groups, Mathematische Zeitschrift 212 (1993), 39-60.MR 94b:20045

[Dou90]
J.M. Douglass, An inversion formula for relative Kazhdan-Lusztig polynomials, Comm. Algebra 18 (1990), 371-387.MR 91c:20064

[Hum90]
James E. Humphreys, Reflection groups and Coxeter groups, Cambridge studies in advanced mathematics, vol. 29, Cambridge University Press, 1990.MR 92h:20002

[Kan87]
M. Kaneda, On the inverse Kazhdan-Lusztig polynomials for affine Weyl groups, J. Reine Angew. Math. 381 (1987), 116-135. MR 89a:20048

[Kat85]
S.I. Kato, On the Kazhdan-Lusztig polynomials for affine Weyl groups, Adv. in Math. 55 (1985), 103-130.MR 86d:20048

[KL79]
David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Inventiones 53 (1979), 191-213.MR 81j:20066

[Lus80a]
George Lusztig, Hecke algebras and Jantzen's generic decomposition patterns, Advances in Mathematics 37 (1980), 121-164.MR 82b:20059

[Lus80b]
George Lusztig, Some problems in the representation theory of finite Chevalley groups, Proceedings of Symposia in Pure Mathematics 37, AMS, 1980, pp. 313-317.MR 82i:20014

[Lus91]
George Lusztig, Intersection cohomology methods in representation theory, Proceedings of the International Congress of Mathematicians 1990 (Ichiro Satake, ed.), Springer, 1991, pp. 155-174.MR 93e:20059

[Mil]
Dragan Milicic, Localization and representation theory of reductive Lie groups, Book in preparation.


Similar Articles:

Retrieve articles in Representation Theory with MSC (1991): 05E99, 17B37

Retrieve articles in all Journals with MSC (1991): 05E99, 17B37


Additional Information:

Wolfgang Soergel
Affiliation: Universität Freiburg, Mathematisches Institut, Eckerstrasse 1, D-79104 Freiburg, Germany
Email: soergel@mathematik.uni-freiburg.de

DOI: 10.1090/S1088-4165-97-00021-6
PII: S 1088-4165(97)00021-6
Received by editor(s): February 4, 1997
Received by editor(s) in revised form: March 17, 1997
Posted: May 5, 1997
Copyright of article: Copyright 1997, By the author


  AMS Website Logo Small Comments: webmaster@ams.org
© Copyright 2008, American Mathematical Society
Privacy Statement
Search the AMSPowered by Google