3:30 pm Thursday, December 9, 2010
Geometry Seminar : Homogeneous vector bundles and quivers by Ada Boralevi (A&M University) in RLM 9.166
A quiver is a directed graph. Quivers come from combinatorics, and homogeneous vector bundles from algebraic geometry. In 1990 Bondal and Kapranov established an equivalence of categories that links together algebraic geometry, representation theory, and combinatorics. To any homogeneous vector bundle on a rational homogeneous variety they associate a finite dimensional representation of a given quiver (with relations). In my talk I will describe this equivalence in detail, and explain how it is an excellent tool for computing cohomology of homogeneous bundles, which leads to a generalization of the well-known Borel-Weil-Bott Theorem. I will then explain a conjectural link of the quiver representations with the Bernstein-Gelfand-Gelfand category O, which could potentially lead to an infinite dimensional version of the above mentioned equivalence. Submitted by
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