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A generalization of Steinberg's cross-section

2011/03/09 by Xuhua He, He, Xuhua, George Lusztig +1
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1103.1769

21 pages

arxiv created 2011/03/09 · arxiv updated 2011/03/10

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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