Homogeneous bundles over abelian varieties and representation theory
Abstract: A vector bundle over an abelian variety X is called homogeneous (or translation-invariant) if it is isomorphic to its pull-back under any translation of X. These vector bundles have been described by Miyanishi and Mukai via methods of algebraic geometry. In this talk, we will first show how to recover their results via representation theory; this also yields new insight in the Fourier-Mukai transform. Then we will generalize this approach to describe the homogeneous principal bundles under a linear algebraic group G; these turn out to be related to the closed commutative subgroups of G.
References : M. B.,
Homogeneous bundles over abelian varieties,
arXiv:1101.2771
Homogeneous projective bundles over abelian varieties,
arXiv:1104.0818