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

2009/11/10 by Ivan Dimitrov, Dimitrov, Ivan, Ivan Penkov +1
Mathematics · #20G05 #22E65 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #math.AG #math.RT #msc:20G05 #msc:22E65

paper · pdf · doi:10.48550/arxiv.0911.1835

20 pages

arxiv created 2009/11/10 · openalex publication_date 2009/11/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Principal series representations of direct limit groups

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