## Twining Character Formula of Borel-Weil-Bott Type

J. Math. Sci. Univ. Tokyo
Vol. 9 (2002), No. 4, Page 637--658.

Naito, Satoshi
Twining Character Formula of Borel-Weil-Bott Type
We prove a twining character formula of Borel-Weil-Bott type for a connected, simply connected, simple affine algebraic group $G$ over $\Bbb C$, by combining a Lefschetz type fixed point formula for the flag variety $G/B$ and a Kostant type twining character formula for the complex simple Lie algebra $\frak g$ of $G$. Our proof is analogous to the well-known "geometric" proof of the Weyl character formula for finite-dimensional irreducible $G$-modules.