Two geometric character formulas for reductive Lie groups

1998/01/18 by Wilfried Schmid, Kari Vilonen
Mathematics · #math.RT #math.AG

paper · pdf

published as J. Amer. Math. Soc. 11 (1998), no. 4, 799-867

arxiv created 1998/01/18 · arxiv updated 2009/11/30

Abstract

In this paper we prove two formulas for the characters of representations of reductive groups. Both express the character of a representation in terms of the same geometric data attached to it. When specialized to the case of a compact Lie group, one of them reduces to Kirillov's character formula in the compact case, and the other, to an application of the Atiyah-Bott fixed point formula to the Borel-Weil realization of the representation.

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