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Two geometric character formulas for reductive Lie groups

Author(s): Wilfried Schmid; Kari Vilonen
Journal: J. Amer. Math. Soc. 11 (1998), 799-867.
MSC (1991): Primary 22Exx, 55-xx, 14-xx
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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
Email: schmid@math.harvard.edu

Kari Vilonen
Affiliation: Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254
Email: vilonen@math.brandeis.edu

DOI: 10.1090/S0894-0347-98-00275-6
PII: S 0894-0347(98)00275-6
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
Copyright of article: Copyright 1998, American Mathematical Society

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