# An Introduction to the Deligne Category $\operatorname{Rep} (S_t)$

## MIT

Abstract

There are many "stability" patterns in the representation theory of symmetric groups. For example, the permutation action of $S_n$ on $\mathbb{C}^n$ decomposes as a direct sum of the trivial representation and the (mean-zero) standard representation (for $n > 1$). Deligne introduced a combinatorial model for representations of symmetric groups which explains this kind of phenomenon. One particularly interesting example is stability of Kronecker coefficients. In this talk we will explain the key parts of the story; partition algebras, the Deligne category $\operatorname{Rep}(S_t)$, and how to prove things about all symmetric groups at once.