A Bott-Borel-Weil theorem for diagonal ind-groups

Ivan Dimitrov; Ivan Penkov

paper

A Bott-Borel-Weil theorem for diagonal ind-groups

arXiv:0911.1835

Abstract

We establish a theorem computing the cohomology groups of line bundles on homogeneous ind-varieties $G / B$ for diagonal ind-groups $G$ . The main difficulty in proving this analog of the classical Bott-Borel-Weil theorem is in defining an appropriate analog $W_{B}$ of the Weyl group so that the action of $W_{B}$ on weights of $G$ is compatible with the analog of the Demazure "action" of the Weyl group on the cohomology of line bundles.

20 pages