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.