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arXiv · 1103.1769

A generalization of Steinberg's cross-section

Xuhua He·George Lusztig
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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.

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Xuhua He, George Lusztig. 2011-03-09. A generalization of Steinberg's cross-section. https://arxiv.org/abs/1103.1769

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