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 Lehmer code of a permutation to $mathcal{OP}_{n, lambda}$.
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机译：让$ k leq n $是非负整数，让$ lambda $ be是$ k $的分区。 S. Griffin最近推出了一个商用R_ {n， lambda} $ mathbb {q} [x_1， dots，x_n] $ n $ n $变量，它同时概括了Haglund的德雷塔猜想币圆环-RHOODES-Shimozono和Tanisaki和Garsia-Procesi学习的弹簧纤维的混沌圈。我们将附加到$ r_ {n， lambda} $的空间$ v_ {n， lambda} $的空间$ r_ {n， lambda} $索引由某些有序集分区$ mathcal索引的$ r_ {n， lambda} $ {op} _ {n， lambda} $。此基础的组合学由Lehmer代码的新扩展为$ mathcal {op} _ {n， lambda} $。
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