Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

A generalization of Steinberg's cross section


Authors: Xuhua He and George Lusztig
Journal: J. Amer. Math. Soc. 25 (2012), 739-757
MSC (2010): Primary 20G99
Published electronically: January 10, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ G$ be a semisimple group over an algebraically closed field. Steinberg has associated to a Coxeter element $ w$ of minimal length $ r$ a subvariety $ V$ of $ G$ isomorphic to an affine space of dimension $ r$ which meets the regular unipotent class $ Y$ in exactly one point. In this paper this is generalized to the case where $ w$ is replaced by any elliptic element in the Weyl group of minimal length $ d$ in its conjugacy class, $ V$ is replaced by a subvariety $ V'$ of $ G$ isomorphic to an affine space of dimension $ d$, and $ Y$ is replaced by a unipotent class $ Y'$ of codimension $ d$ in such a way that the intersection of $ V'$ and $ Y'$ is finite.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Journal of the American Mathematical Society with MSC (2010): 20G99

Retrieve articles in all journals with MSC (2010): 20G99


Additional Information

Xuhua He
Affiliation: Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong

George Lusztig
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307

DOI: http://dx.doi.org/10.1090/S0894-0347-2012-00728-0
PII: S 0894-0347(2012)00728-0
Received by editor(s): March 14, 2011
Received by editor(s) in revised form: October 4, 2011, and December 5, 2011
Published electronically: January 10, 2012
Additional Notes: The first author was supported in part by HKRGC grant 601409
The second author was supported in part by National Science Foundation grant DMS-0758262
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.