Elliptic elements in a Weyl group: a homogeneity property
HTML articles powered by AMS MathViewer
- by G. Lusztig
- Represent. Theory 16 (2012), 127-151
- DOI: https://doi.org/10.1090/S1088-4165-2012-00409-5
- Published electronically: February 20, 2012
- PDF | Request permission
Abstract:
Let $G$ be a reductive group over an algebraically closed field whose characteristic is not a bad prime for $G$. Let $w$ be an elliptic element of the Weyl group which has minimum length in its conjugacy class. We show that there exists a unique unipotent class $X$ in $G$ such that the following holds: if $V$ is the variety of pairs $(g,B)$ where $g\in X$ and $B$ is a Borel subgroup such that $B,gBg^{-1}$ are in relative position $w$, then $V$ is a homogeneous $G$-space.References
- 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
- Meinolf Geck, Gerhard Hiss, Frank Lübeck, Gunter Malle, and Götz Pfeiffer, CHEVIE—a system for computing and processing generic character tables, Appl. Algebra Engrg. Comm. Comput. 7 (1996), no. 3, 175–210. Computational methods in Lie theory (Essen, 1994). MR 1486215, DOI 10.1007/BF01190329
- 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
- D. F. Holt and N. Spaltenstein, Nilpotent orbits of exceptional Lie algebras over algebraically closed fields of bad characteristic, J. Austral. Math. Soc. Ser. A 38 (1985), no. 3, 330–350. MR 779199, DOI 10.1017/S1446788700023636
- G. Lusztig, Intersection cohomology complexes on a reductive group, Invent. Math. 75 (1984), no. 2, 205–272. MR 732546, DOI 10.1007/BF01388564
- 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. Luszrig, From conjugacy classes in the Weyl group to unipotent classes, Represent. Theory 15 (2011), 494–530.
- F. Lübeck, http://www.math.rwth-aachen.de/Frank.Luebeck/chev/Green/.
- 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
Bibliographic Information
- G. Lusztig
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 117100
- Received by editor(s): January 13, 2011
- Received by editor(s) in revised form: June 17, 2011
- Published electronically: February 20, 2012
- Additional Notes: Supported in part by the National Science Foundation
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Represent. Theory 16 (2012), 127-151
- MSC (2010): Primary 20G99
- DOI: https://doi.org/10.1090/S1088-4165-2012-00409-5
- MathSciNet review: 2888173