Two geometric character formulas for reductive Lie groups

Schmid, Wilfried¹ ; Vilonen, Kari²

¹Department of Mathematics, Harvard University, Cambridge, Massachusetts 02138
²Department of Mathematics, Brandeis University, Waltham, Massachusetts 02254

Journal of the American Mathematical Society, Tome 11 (1998) no. 4, pp. 799-867

Résumé

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 $\pi$.

Détail

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

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