Séance Séminaire

Séminaire Algèbre Géométrie Algébrique Topologie Algébrique

Transversal index and geometric quantization.

If a compact connected Lie group acts holomorphically on a holomorphic line bundle on a complete Kahler manifold, in many situations, the associated cohomology group is infinite dimensional, but the multiplicity of each irreducible representation of $G$ in the cohomology group is finite. In this talk, we are interested in how to compute the multiplicities in a geometric way. We will explain our solution of a version of this kind problem formulated by Michele Vergne in her ICM 2006 plenary lecture in symplectic geometry. This is a joint work wth Weiping Zhang.