Stable bundles, representation theory, and Hermitian operators

Alexander Klyachko

In the talk we'll explain connections between the following apparently disjoint problems:

i) Existence of Hermite-Einstein metric on a stable bundle.
ii) Decomposition of a tensor product of irreducible representations of group SU(n).
iii) A sharp estimation of spectrum of a sum of Hermitian operators with given spectra.

Similar problems for other structure groups will be considered.