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Ordered set partitions, Garsia-Procesi modules, and rank varieties

Sean Griffin, University of Washington
Wednesday, May 27, 2020 - 3:30pm to 5:00pm
Via Zoom
Sean Griffin

Note: This talk begins with a pre-seminar (aimed at graduate students) at 3:30–4:00. The main talk starts at 4:10.

Coinvariant rings \$R_n\$ are a well-studied family of rings with rich connections to the combinatorics of the symmetric group \$S_n\$. Two remarkable families of graded rings which generalize the coinvariant rings are:

  • The cohomology rings of Springer fibers \$R_\lambda\$, whose \$S_n\$-module structure coincides with the dual Hall-Littlewood functions under the graded Frobenius characteristic map.
  • The generalized coinvariant rings \$R_{n,k}\$ of Haglund, Rhoades, and Shimozono, which give a representation-theoretic interpretation of the expression in the Delta Conjecture when \$t=0\$.

In this talk, we introduce a family of graded rings \$R_{n,\lambda,s}\$ which are a common generalization of \$R_\lambda\$ and \$R_{n,k}\$. We then generalize many of the previously known formulas for \$R_{\lambda}\$ and \$R_{n,k}\$ to our setting. Finally, we show how our results can be applied to Eisenbud-Saltman rank varieties, generalizing work of De Concini-Procesi and Tanisaki.


The UW combinatorics seminar is inviting you to a scheduled Zoom meeting.

Topic: UW combinatorics seminar: Sean Griffin
Time: May 27, 2020 03:30 PM Pacific Time (US and Canada)

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