## 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:

 2.2e+46 Representations of Lie and linear algebraic groups over real fields: analytic methods
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### References:

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