# Colloquium abstracts

**Amritanshu Prasad***

The Institute of Mathematical Sciences, Chennai

June 18, 2020

**On the restriction of polynomial representations of GL(n) to S(n)**: The polynomial representations of GL(n) and the representations of S(n) have been well-understood for over 100 years due to the work of Frobenius, Schur, and Weyl. However, the determination of the decomposition into irreducible representations of S(n) of an irreducible polynomial representation of GL(n) remains an open problem in algebraic combinatorics, in the same league as the notorious Kronecker problem. This problem leads to interesting questions in the theory of symmetric polynomials and enumerative combinatorics. In this talk, I will describe some attempts at solving this problem.