Restricting Howe Duality

Abstract: Classical Howe duality provides a representation theoretic framework for classical invariant theory. In the classical Howe duality, the general linear group, $GL_n(\mathbb{C})$, is the dual to $GL_n(\mathbb{C})$ when acting on the polynomial ring of the variables $x_{i,j}$ where $1\leq i \leq n$ and $1\leq j \leq k$. In this talk, I will introduce a multiset partition algebra, MP_k(n), as the Howe dual to the action of the symmetric group, $S_n$, on the polynomial ring.\

combinatorics

Audience: researchers in the topic

York University Applied Algebra Seminar