Colloquium abstracts

Shraddha Srivastava*
TIFR, Mumbai
May 14, 2020

On internal tensor products of representations of the general linear group and the symmetric group:  A polynomial representation of the general linear group GL_n(K) of degree d is equivalent to a module over the centralizer algebra, called the classical Schur algebra S(n,d), of symmetric group S_d acting on the d-fold tensor product of K^n, for an infinite field K. Strict polynomial functors of degree d, introduced by Friedlander and Suslin, uniformly encapsulate the modules over S(n,d) across all n. Krause exhibited an internal tensor product of strict polynomial functors of degree d. In this talk, we will show that the Schur functor, induced from the classical Schur--Weyl duality, takes the internal tensor product of strict polynomial functors of degree d to the Kronecker product of representations of S_d. We will also compute the internal tensor involving classical exponential functors, e.g., symmetric power, divided power, and exterior power functors.