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Harmonic Bases for Generalized Coinvariant Algebras by Rhoades, Brendon; Yu, Tianyi; Zhao, Zehong is a scholarly article available to read on EtoBox.

What is Harmonic Bases for Generalized Coinvariant Algebras about?

Let $k \leq n$ be nonnegative integers and let $\lambda$ be a partition of $k$. S. Griffin recently introduced a quotient $R_{n,\lambda}$ of the polynomial ring $\mathbb{Q}[x_1, \dots, x_n]$ in $n$ variables which simultaneously generalizes the Delta Conjecture coinvariant rings of Haglund-Rhoades-Shimozono and the cohomology rings of Springer fibers studied by Tanisaki and Garsia-Procesi. We describe the space $V_{n,\lambda}$ of harmonics attached to $R_{n,\lambda}$ and produce a harmonic basis of $R_{n,\lambda}$ indexed by certain ordered set partitions $\mathcal{OP}_{n,\lambda}$. The combinatorics of this basis is governed by a new extension of the {\em Lehmer code} of a permutation to $\mathcal{OP}_{n, \lambda}$.

Author

Rhoades, Brendon; Yu, Tianyi; Zhao, Zehong

Published

2020

Language

EN