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Two geometric character formulas for reductive Lie groups

Wilfried Schmid·Kari Vilonen
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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 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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Wilfried Schmid, Kari Vilonen. 1998-01-18. Two geometric character formulas for reductive Lie groups. https://arxiv.org/abs/math/9801081

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