##### Department of Mathematics,

University of California San Diego

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### Advancement to Candidacy

## Jesse Kim

#### UCSD

## A combinatorial model for the fermionic diagonal coinvariant ring

##### Abstract:

The fermionic diagonal coinvariant ring was introduced by Rhoades and Jongwon Kim and is a quotient of a polynomial ring in two sets of $n$ anticommuting variables modulo $\mathfrak{S}_n$ invariant polynomials with no constant term, where the action of $\mathfrak{S}_n$ permutes both sets of variables simultaneously. In this talk, we will introduce a basis of this ring for which the action of $\mathfrak{S}_{n-1} \subset \mathfrak{S}_n$ can be interpreted combinatorially and use this basis to determine the isomorphism type of the ring. We will also relate our basis to a cyclic sieving result by Thiel.

Advisor: Brendon Rhoades

### February 17, 2022

### 3:00 PM

Zoom ID: 918 8760 6616

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