Skip to Content

Sponsors

No results

Keywords

No results

Types

No results

Search Results

Events

No results
Search events using: keywords, sponsors, locations or event type
When / Where

Presented By: Combinatorics Seminar - Department of Mathematics

Representation stability via Young symmetrizers and a new ribbon basis for the rank-selected homology of the partition lattice (Combinatorics seminar)

Patricia Hersh (University of Oregon)

In this talk, we will begin with a quick review of group actions on posets, rank-selected homology of posets, representation stability, and a nice way of interpreting the rank-selected homology of the Boolean lattice as a Specht module of ribbon shape. This interpretation allows us to prove a sharp representation stability bound for the rank-selected homology of the Boolean lattice. We then describe a new ​ribbon basis for the rank-selected homology of any geometric lattice. In the case of the partition lattice, this ribbon basis interacts with Young symmetrizers in much the way a traditional Specht module would. Using this basis, we prove a sharp representation stability bound for the rank-selected homology of the partititon lattice, a bound that had previously been conjectured by the speaker and Vic Reiner. This is joint work with Sheila Sundaram.

Explore Similar Events

  •  Loading Similar Events...

Keywords


Back to Main Content