Return to Colloquia & Seminar listing
Representations of the symmetric groups and cohomology
Algebra & Discrete Mathematics| Speaker: | Sarah Witherspoon, MSRI and TAMU |
| Location: | 693 Kerr |
| Start time: | Fri, Mar 5 2004, 12:10PM |
Description
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.