École polytechnique  – Centre de Mathématiques Laurent Schwartz

Mardi 28 novembre 2023

14h00 : Shrawan Kumar (University of North Carolina at Chapel Hill)

"Tensor product decomposition "

Let G be a semisimple connected complex algebraic group. We choose a Borel subgroup B and a maximal torus T in B. The irreducible finite-dimensional representations of G are parametrized by the set of dominant characters of T. 
Any tensor product of two irreducible finite-dimensional representation can be written as a direct sum of irreducible finite representations with multiplicities. These multiplicities are called Littlewood-Richardson coefficients.
We say that an irreducible representation occurs in some tensor product if its multiplicity is positive.

One of the major goals of the ‘tensor product problem’ is to determine (all) irreducible representations occurring in a given tensor product. Of course, a more refined problem is to determine these representations together with their multiplicities. In general, even the first problem is very hard. 
There is also a weaker "saturated tensor product problem".
The aim of this talk is to give an overview of some of our results on the tensor product decomposition obtained individually or jointly with others.