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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Two geometric character formulas
for reductive Lie groups


Authors: Wilfried Schmid and Kari Vilonen
Journal: J. Amer. Math. Soc. 11 (1998), 799-867
MSC (1991): Primary 22Exx, 55-xx, 14-xx
MathSciNet review: 1612634
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Abstract | References | Similar Articles | Additional Information

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: http://dx.doi.org/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
Article copyright: © Copyright 1998 American Mathematical Society