Character Polynomials for Symmetric Groups and FI-modules

Abstract: For every positive integer $r$, the number of cycles of length $r$ in the cycle decomposition of a permutation is a class function $X_r$ which is simultaneously defined on every symmetric group. A polynomial in terms of $X_r$'s is called a character polynomial, describing a sequence of (virtual) $S_n$ representations for every $n$. In this talk I will discuss how such sequences arise in particular examples of interest and time permitting explain how the theory of FI-modules provides a general framework for their occurrence.

Mathematics

Audience: researchers in the topic

METU Mathematics General Seminar