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Syu Kato

Equivariant vector bundles on group completions

In this paper, we describe the category of bi-equivariant vector bundles on a bi-equivariant smooth (partial) compactification of a connected reductive algebraic group with normal crossing boundary divisors. Our result is a generalization of the description of the category of equivariant vector bundles on toric varieties established by A. A. Klyachko (Math. USSR Izvest. 35 No. 2 (1990)). As an application, we prove splitting of equivariant vector bundles of low rank on the wonderful compactification of an adjoint simple group in the sense of C. De Concini and C. Procesi (Lect. Notes Math. 996 (1983)). Moreover, we present an answer to a problem raised by B. Kostant in the case of complex groups.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2005, 04/2005
Pages: 71 - 116

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