## A generalization of Steinberg’s cross section

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- by Xuhua He and George Lusztig
- J. Amer. Math. Soc.
**25**(2012), 739-757 - DOI: https://doi.org/10.1090/S0894-0347-2012-00728-0
- Published electronically: January 10, 2012
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## 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

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## Bibliographic 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
- MR Author ID: 117100
- 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 - © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc.
**25**(2012), 739-757 - MSC (2010): Primary 20G99
- DOI: https://doi.org/10.1090/S0894-0347-2012-00728-0
- MathSciNet review: 2904572