Two geometric character formulas for reductive Lie groups
Abstract
In this paper we prove two formulas for the characters of representations of reductive groups. Both express the character of a representation in terms of the same geometric data attached to it. 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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- January 1998
- DOI:
- 10.48550/arXiv.math/9801081
- arXiv:
- arXiv:math/9801081
- Bibcode:
- 1998math......1081S
- Keywords:
-
- Representation Theory;
- Algebraic Geometry
- E-Print:
- J. Amer. Math. Soc. 11 (1998), no. 4, 799-867