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Kazhdan-Lusztig-Polynome und eine Kombinatorik für Kipp-Moduln

Author: Wolfgang Soergel
Journal: Represent. Theory 1 (1997), 37-68
MSC (1991): Primary 05E99, 17B37
Published electronically: March 7, 1997
English translation: Represent. Theory 1 (1997)
MathSciNet review: 1445511
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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.

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  • [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, 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.

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Additional Information

Wolfgang Soergel
Affiliation: Universität Freiburg, Mathematisches Institut, Eckerstrasse 1, D-79104 Freiburg, Germany

Received by editor(s): September 25, 1996
Received by editor(s) in revised form: January 2, 1997
Published electronically: March 7, 1997
Article copyright: © Copyright 1997 By the author

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