余不变环推广的更高Specht基
Higher Specht bases for generalizations of the coinvariant ring
AI总结：
本文为广义余不变环 $R_{n,k}$ 和Garsia-Procesi模 $R_\mu$ 的推广构造了更高Specht基，并证明了两行分区情形下的猜想，进而为Griffin定义的 $R_{n,k,\mu}$ 无限子族提供了基。
摘要：
经典余不变环 $R_n$ 定义为 $n$ 个变量的多项式环模去正次数 $S_n$-不变量的商环。它有一个已知的基，该基尊重 $R_n$ 分解为不可约 $S_n$-模的分解，由Ariki、Terasoma和Yamada提出的更高Specht多项式组成。我们将更高Specht基推广到广义余不变环 $R_{n,k}$。我们还给出了Garsia-Procesi模 $R_\mu$ 的一个猜想性更高Specht基，并在两行分区形状 $\mu$ 的情况下证明了该猜想。然后，我们结合这些结果，为Griffin最近定义的模 $R_{n,k,\mu}$ 的一个无限子族提供了更高Specht基，该子族是 $R_{n,k}$ 和 $R_\mu$ 的公共推广。
英文摘要：
The classical coinvariant ring $R_n$ is defined as the quotient of a polynomial ring in $n$ variables by the positive-degree $S_n$-invariants. It has a known basis that respects the decomposition of $R_n$ into irreducible $S_n$-modules, consisting of the higher specht polynomials due to Ariki, Terasoma, and Yamada. We provide an extension of the higher Specht basis to the generalized coinvariant rings $R_{n,k}$. We also give a conjectured higher Specht basis for the Garsia-Procesi modules $R_μ$, and provide a proof of the conjecture in the case of two-row partition shapes $μ$. We then combine these results to give a higher Specht basis for an infinite subfamily of the modules $R_{n,k,μ}$ recently defined by Griffin, which are a common generalization of $R_{n,k}$ and $R_μ$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
