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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

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From conjugacy classes in the Weyl group to unipotent classes
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by G. Lusztig
Represent. Theory 15 (2011), 494-530
DOI: https://doi.org/10.1090/S1088-4165-2011-00396-4
Published electronically: June 8, 2011
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Abstract:

Let $G$ be a connected reductive algebraic group over an algebraic closed field. We define a (surjective) map from the set of conjugacy classes in the Weyl group to the set of unipotent classes in $G$.
References
  • R. W. Carter, Conjugacy classes in the Weyl group, Compositio Math. 25 (1972), 1–59. MR 318337
  • P. Deligne and G. Lusztig, Representations of reductive groups over finite fields, Ann. of Math. (2) 103 (1976), no. 1, 103–161. MR 393266, DOI 10.2307/1971021
  • Erich W. Ellers and Nikolai Gordeev, Intersection of conjugacy classes with Bruhat cells in Chevalley groups, Pacific J. Math. 214 (2004), no. 2, 245–261. MR 2042932, DOI 10.2140/pjm.2004.214.245
  • Meinolf Geck, On the average values of the irreducible characters of finite groups of Lie type on geometric unipotent classes, Doc. Math. 1 (1996), No. 15, 293–317. MR 1418951
  • M.Geck, G.Hiss, F.Lübeck, G.Malle and G.Pfeiffer, A system for computing and processing generic character tables for finite groups of Lie type, Weyl groups and Hecke algebras, Appl. Algebra Engrg. Comm. Comput. 7 (1996), 175-210.
  • Meinolf Geck and Götz Pfeiffer, Characters of finite Coxeter groups and Iwahori-Hecke algebras, London Mathematical Society Monographs. New Series, vol. 21, The Clarendon Press, Oxford University Press, New York, 2000. MR 1778802
  • Noriaki Kawanaka, Unipotent elements and characters of finite Chevalley groups, Osaka Math. J. 12 (1975), no. 2, 523–554. MR 384914
  • D. Kazhdan and G. Lusztig, Fixed point varieties on affine flag manifolds, Israel J. Math. 62 (1988), no. 2, 129–168. MR 947819, DOI 10.1007/BF02787119
  • G.Lusztig, On the reflection representation of a finite Chevalley group, Representation theory of Lie groups, LMS Lect. Notes Ser. 34, Cambridge Univ. Press, 1979, pp. 325-337.
  • George Lusztig, Characters of reductive groups over a finite field, Annals of Mathematics Studies, vol. 107, Princeton University Press, Princeton, NJ, 1984. MR 742472, DOI 10.1515/9781400881772
  • George Lusztig, Character sheaves. V, Adv. in Math. 61 (1986), no. 2, 103–155. MR 849848, DOI 10.1016/0001-8708(86)90071-X
  • George Lusztig, Green functions and character sheaves, Ann. of Math. (2) 131 (1990), no. 2, 355–408. MR 1043271, DOI 10.2307/1971496
  • G. Lusztig, Hecke algebras with unequal parameters, CRM Monograph Series, vol. 18, American Mathematical Society, Providence, RI, 2003. MR 1974442, DOI 10.1090/crmm/018
  • G.Lusztig, On some partitions of a flag manifold, arxiv:0906.1505.
  • F.Lübeck, http://www.math.rwth-aachen.de/~Frank.Luebeck /chev/Green/.
  • Kenzo Mizuno, The conjugate classes of unipotent elements of the Chevalley groups $E_{7}$ and $E_{8}$, Tokyo J. Math. 3 (1980), no. 2, 391–461. MR 605099, DOI 10.3836/tjm/1270473003
  • Toshiaki Shoji, Character sheaves and almost characters of reductive groups. I, II, Adv. Math. 111 (1995), no. 2, 244–313, 314–354. MR 1318530, DOI 10.1006/aima.1995.1024
  • Nicolas Spaltenstein, Classes unipotentes et sous-groupes de Borel, Lecture Notes in Mathematics, vol. 946, Springer-Verlag, Berlin-New York, 1982 (French). MR 672610, DOI 10.1007/BFb0096302
  • N. Spaltenstein, On the generalized Springer correspondence for exceptional groups, Algebraic groups and related topics (Kyoto/Nagoya, 1983) Adv. Stud. Pure Math., vol. 6, North-Holland, Amsterdam, 1985, pp. 317–338. MR 803340, DOI 10.2969/aspm/00610317
  • N. Spaltenstein, Polynomials over local fields, nilpotent orbits and conjugacy classes in Weyl groups, Astérisque 168 (1988), 10–11, 191–217. Orbites unipotentes et représentations, I. MR 1021497
  • N. Spaltenstein, On the Kazhdan-Lusztig map for exceptional Lie algebras, Adv. Math. 83 (1990), no. 1, 48–74. MR 1069387, DOI 10.1016/0001-8708(90)90068-X
  • Robert Steinberg, Regular elements of semisimple algebraic groups, Inst. Hautes Études Sci. Publ. Math. 25 (1965), 49–80. MR 180554, DOI 10.1007/BF02684397
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Bibliographic Information
  • G. Lusztig
  • Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
  • MR Author ID: 117100
  • Received by editor(s): April 22, 2010
  • Received by editor(s) in revised form: August 11, 2010
  • Published electronically: June 8, 2011
  • Additional Notes: Supported in part by the National Science Foundation
  • © Copyright 2011 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Represent. Theory 15 (2011), 494-530
  • MSC (2010): Primary 20G99
  • DOI: https://doi.org/10.1090/S1088-4165-2011-00396-4
  • MathSciNet review: 2833465