Geodesic
A generalization of Steinberg’s cross section
He, Xuhua1 ; Lusztig, George2
1 Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307
Journal of the American Mathematical Society, Tome 25 (2012) no. 3, pp. 739-757 Cet article a éte moissonné depuis la source American Mathematical Society

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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.
DOI : 10.1090/S0894-0347-2012-00728-0

He, Xuhua 1 ; Lusztig, George 2

1 Department of Mathematics, Hong Kong University of Science and Technology, Hong Kong
2 Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139-4307 
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He, Xuhua; Lusztig, George. A generalization of Steinberg’s cross section. Journal of the American Mathematical Society, Tome 25 (2012) no. 3, pp. 739-757. doi: 10.1090/S0894-0347-2012-00728-0

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