Speaker:
Sarah Witherspoon, Texas A&M University
Title:
Representations of the symmetric groups and cohomology
Abstract:
The permutation representation of $S_n$ on $C^{2n}$, and the corresponding
quotient space $C^{2n}/S_n$, are examples of great interest in combinatorics
and geometry. The corresponding action of $S_n$ on either the polynomial ring
$C[x_1,y_1,...,x_n,y_n]$ or a Weyl algebra, and the resulting invariant
subrings and crossed product rings, are algebraically interesting. In either
context, there are cohomology rings encoding important information that have
combinatorial descriptions. In this talk, we will describe the structures of
certain Hochschild and orbifold cohomology rings for these examples, and
mention more general results involving arbitrary finite group actions on
vector spaces.
No knowledge of cohomology will be required: All cohomology rings will be
introduced and motivated during the talk.
