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

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

2009-11-10

arxiv.org/abs/0911.1835v1

Mathematics

Algebraic Geometry

20 pages

Scientific paper

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.

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