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Two geometric character formulas for reductive Lie groups. (English) Zbl 0976.22010
Summary: 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 \(\pi\).

MSC:
22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
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