论文标题
通用共同代数的谐波基础
Harmonic bases for generalized coinvariant algebras
论文作者
论文摘要
令$ k \ leq n $为非负整数，让$λ$为$ k $的分区。 S. Griffin最近引入了多项式环$ \ Mathbb {q} [x_1，\ dots，x_n] $ n $ n $变量的商$ r_ {塔尼萨基和加西亚 - 普罗维西。我们描述了附加到$ r_ {n，λ} $的谐波的空间$ v_ {n，λ} $，并产生$ r_ {n，λ} $的谐波基础，该基础由某些有序的集合分区索引$ \ MATHCAL {OP} _ {op} _ {n，λ} $。此基础的组合由定量{\ em Lehmer code}的新扩展为$ \ MATHCAL {op} _ {n，λ} $的新扩展。
Let $k \leq n$ be nonnegative integers and let $λ$ be a partition of $k$. S. Griffin recently introduced a quotient $R_{n,λ}$ 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 $V_{n,λ}$ of harmonics attached to $R_{n,λ}$ and produce a harmonic basis of $R_{n,λ}$ indexed by certain ordered set partitions $\mathcal{OP}_{n,λ}$. The combinatorics of this basis is governed by a new extension of the {\em Lehmer code} of a permutation to $\mathcal{OP}_{n, λ}$.
