Elliptic elements in a Weyl group: a homogeneity property

Details Elliptic elements in a Weyl group: a homogeneity property Elliptic elements in a Weyl group: a homogeneity property

2010-07-28

arxiv.org/abs/1007.5040v2

Mathematics

Representation Theory

29 pages; a new section added

Scientific paper

Let G be a reductive group over an algebraically closed field whose characteristic is not a bad prime for G. Let w be an elliptic element of the Weyl group which has minimal length in its conjugacy class. We show that there exists a unique unipotent class X in G such that the following holds: if V is the variety of pairs consisting of an element g in X and a Borel subgroup B such that B,gBg^{-1} are in relative position w, then V is a homogeneous G-space.

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