Two geometric character formulas for reductive Lie groups

Schmid, Wilfried; Vilonen, Kari

doi:10.1090/S0894-0347-98-00275-6

Two geometric character formulas for reductive Lie groups
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by Wilfried Schmid and Kari Vilonen

J. Amer. Math. Soc. 11 (1998), 799-867

DOI: https://doi.org/10.1090/S0894-0347-98-00275-6

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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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Two geometric character formulas for reductive Lie groups
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Abstract: