论文标题
较高的SpepHT基础，用于共同环的概括
Higher Specht bases for generalizations of the coinvariant ring
论文作者
论文摘要
经典共同环$ r_n $定义为$ n $变量在$ n $变量中由正数$ s_n $ -invariants的商。它的已知基础尊重$ r_n $在不可约$ s_n $模块中的分解，由由于Ariki，Terosoma和Yamada而引起的较高SpecHT多项式组成。 我们向广义共旋转环$ r_ {n，k} $提供了更高的规格基础的扩展名。我们还为GARSIA-PROCESI模块$R_μ$提供了较高的Specht基础，并在两排分区形状$μ$的情况下提供了猜想的证明。然后，我们将这些结果结合起来，为Griffin最近定义的模块$ r_ {n，k，μ} $的无限亚家族提供更高的规格基础，这是$ r_ {n，k} $和$r_μ$的常见概括。
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 $R_μ$.
