Equivariant vector bundles on group completions
Abstract
Description
In this paper, we describe the category of bi-equivariant vector bundles on a bi-equivariant smooth (partial) compactification of a 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. Izvestiya, {\bf 35}, No.2 (1990)]. As an application, we prove splitting of equivariant vector bundles of low rank on the wonderful compactification of an adjoint semisimple group in the sense of C. De Concini and C. Procesi [Lecture Note in Math. {\bf 996} (1983)]. Moreover, we present an answer to a problem raised by B. Kostant in the case of complex groups.
Final version. Improved Exposition. to appear in Crelle's J. 43pages
Final version. Improved Exposition. to appear in Crelle's J. 43pages