|
Kazhdan-Lusztig-Polynome und eine Kombinatorik für Kipp-Moduln
Author:
Wolfgang Soergel
Journal:
Represent. Theory 1 (1997), 37-68
MSC (1991):
Primary 05E99, 17B37
Posted:
March 7, 1997
English translation:
Represent. Theory 1 (1997)
MathSciNet review:
1445511
Full-text PDF Free Access
Abstract |
References |
Similar Articles |
Additional Information
Abstract: This article gives a selfcontained 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.
- [AJS94]
H.
H. Andersen, J.
C. Jantzen, and W.
Soergel, Representations of quantum groups at a 𝑝th 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
(95j:20036)
- [And86]
Henning
Haahr Andersen, An inversion formula for the Kazhdan-Lusztig
polynomials for affine Weyl groups, Adv. in Math. 60
(1986), no. 2, 125–153. MR 840301
(87j:22025), http://dx.doi.org/10.1016/S0001-8708(86)80008-1
- [And92]
Henning
Haahr Andersen, Tensor products of quantized tilting modules,
Comm. Math. Phys. 149 (1992), no. 1, 149–159.
MR
1182414 (94b:17015)
- [And96]
Henning Haahr Andersen, Filtrations and tilting modules, Aarhus Preprint No 7, 1996.
- [BGS96]
Alexander
Beilinson, Victor
Ginzburg, and Wolfgang
Soergel, Koszul duality patterns in
representation theory, J. Amer. Math. Soc.
9 (1996), no. 2,
473–527. MR 1322847
(96k:17010), http://dx.doi.org/10.1090/S0894-0347-96-00192-0
- [Bou81]
Nicolas
Bourbaki, Éléments de mathématique,
Masson, Paris, 1981 (French). Groupes et algèbres de Lie. Chapitres
4, 5 et 6. [Lie groups and Lie algebras. Chapters 4, 5 and 6]. MR 647314
(83g:17001)
- [Deo87]
Vinay
V. Deodhar, On some geometric aspects of Bruhat orderings. II. The
parabolic analogue of Kazhdan-Lusztig polynomials, J. Algebra
111 (1987), no. 2, 483–506. MR 916182
(89a:20054), http://dx.doi.org/10.1016/0021-8693(87)90232-8
- [Deo91]
Vinay
V. Deodhar, Duality in parabolic set up for questions in
Kazhdan-Lusztig theory, J. Algebra 142 (1991),
no. 1, 201–209. MR 1125213
(92j:20049), http://dx.doi.org/10.1016/0021-8693(91)90225-W
- [Deo94]
Vinay
Deodhar, A brief survey of Kazhdan-Lusztig theory and related
topics, (University Park, PA, 1991) Proc. Sympos. Pure Math.,
vol. 56, Amer. Math. Soc., Providence, RI, 1994,
pp. 105–124. MR 1278702
(96d:20039)
- [Don93]
Stephen
Donkin, On tilting modules for algebraic groups, Math. Z.
212 (1993), no. 1, 39–60. MR 1200163
(94b:20045), http://dx.doi.org/10.1007/BF02571640
- [Dou90]
J.
Matthew Douglass, An inversion formula for relative Kazhdan-Lusztig
polynomials, Comm. Algebra 18 (1990), no. 2,
371–387. MR 1047315
(91c:20064), http://dx.doi.org/10.1080/00927879008823919
- [Hum90]
James
E. Humphreys, Reflection groups and Coxeter groups, Cambridge
Studies in Advanced Mathematics, vol. 29, Cambridge University Press,
Cambridge, 1990. MR 1066460
(92h:20002)
- [Kan87]
Masaharu
Kaneda, On the inverse Kazhdan-Lusztig polynomials for affine Weyl
groups, J. Reine Angew. Math. 381 (1987),
116–135. MR
918844 (89a:20048), http://dx.doi.org/10.1515/crll.1987.381.116
- [Kat85]
Shin-ichi
Kato, On the Kazhdan-Lusztig polynomials for affine Weyl
groups, Adv. in Math. 55 (1985), no. 2,
103–130. MR
772611 (86d:20048), http://dx.doi.org/10.1016/0001-8708(85)90017-9
- [KL79]
David
Kazhdan and George
Lusztig, Representations of Coxeter groups and Hecke algebras,
Invent. Math. 53 (1979), no. 2, 165–184. MR 560412
(81j:20066), http://dx.doi.org/10.1007/BF01390031
- [Lus80a]
George
Lusztig, Hecke algebras and Jantzen’s generic decomposition
patterns, Adv. in Math. 37 (1980), no. 2,
121–164. MR
591724 (82b:20059), http://dx.doi.org/10.1016/0001-8708(80)90031-6
- [Lus80b]
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
(82i:20014)
- [Lus91]
George
Lusztig, Intersection cohomology methods in representation
theory, II (Kyoto, 1990) Math. Soc. Japan, Tokyo, 1991,
pp. 155–174. MR 1159211
(93e:20059)
- [Mil]
Dragan Mili\v{c}i\'{c}, Localization and representation theory of reductive Lie groups, Book in preparation.
- [AJS94]
- Henning Haahr Andersen, Jens Carsten Jantzen, and Wolfgang Soergel, Representations of quantum groups at a
-th root of unity and of semisimple groups in characteristic : Independence of , 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, Amer. Math. Soc., 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, Amer. Math. Soc., 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 Mili\v{c}i\'{c}, Localization and representation theory of reductive Lie groups, Book in preparation.
Similar Articles
Retrieve articles in Representation Theory of the American Mathematical Society
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:
http://dx.doi.org/10.1090/S1088-4165-97-00006-X
PII:
S 1088-4165(97)00006-X
Received by editor(s):
September 25, 1996
Received by editor(s) in revised form:
January 2, 1997
Posted:
March 7, 1997
Article copyright:
© Copyright 1997 By the author
|