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
DOI:
https://doi.org/10.1090/S0894-0347-98-00275-6
MathSciNet review:
1612634
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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
MR Author ID:
178620
Email:
vilonen@math.brandeis.edu
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