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比利时vs摩洛哥足彩 ,
university of california san diego

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math 269 -combinatorics seminar

tianyi yu

uc san diego

harmonic bases for generalized coinvariant algebras

abstract:

s. griffin introduced a quotient $r_{n,\lambda}$ of the polynomial ring $\mathbb{q}$ with $\mathbb{q}$. it 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 $\mathcal{op}_{n,\lambda}$. our description of $v_{n,\lambda}$ involves injective tableaux and vandermonde determinants. combinatorics of our harmonic basis is governed by a new extension of the lemher code. \\ \\ this is a joint work with brendon rhoades and zehong zhao.

june 3, 2021

3:00 pm

https://ucsd.zoom.us/j/98781502962

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