Speaker: Shraddha Srivastava
Date: May 14, 2020
Affiliation: TIFR, Mumbai

Abstract: 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.