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Two geometric character formulas
for reductive Lie groups

Authors: Wilfried Schmid and Kari Vilonen
Journal: J. Amer. Math. Soc. 11 (1998), 799-867
MSC (1991): Primary 22Exx, 55-xx, 14-xx
MathSciNet review: 1612634
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Abstract: In this paper we prove two formulas for the characters of representations of reductive groups. Both express the character of a representation $\pi $ in terms of the same geometric data attached to $\pi $. 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 $\pi $.

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Additional Information

Wilfried Schmid
Affiliation: Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138

Kari Vilonen
Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254

Received by editor(s): July 24, 1997
Additional Notes: The first author was partially supported by the NSF
The second author was partially supported by the NSA and NSF
Article copyright: © Copyright 1998 American Mathematical Society

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