Higher Specht Bases for Generalizations of the Coinvariant Ring
Higher Specht Bases for Generalizations of the Coinvariant Ring
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DOI：
10.1007/s00026-020-00516-1
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发表时间：
2020-05
影响因子：
0.5
通讯作者：
M. Gillespie;B. Rhoades
中科院分区：
文献类型：
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作者：
M. Gillespie;B. Rhoades
经典的上不变环定义为多项式环的不变元与正度不变元的商。它有一个已知的基础，尊重分解的into不可约模，由更高的Specht多项式由于Ariki，Terasoma，和山田（广岛数学J 27（1）：177-188，1997）。我们提供了Haglund等人（Adv Math 329：851-915，2018）中引入的广义协不变环的高阶Specht基的扩展。我们还给出了Garsia-Procesi模的一个严格的高阶Specht基，并在两行分割形状的情形下证明了这个猜想.然后，我们结合联合收割机这些结果，给出一个更高的Specht基础的无限子族的modulesrecently定义的格里芬（transamer数学学会，出现，2020年），这是一个共同的推广和。
The classical coinvariant ringis defined as the quotient of a polynomial ring innvariables by the positive-degree-invariants. It has a known basis that respects the decomposition ofinto irreducible-modules, consisting of thehigher Specht polynomialsdue to Ariki, Terasoma, and Yamada (Hiroshima Math J 27(1):177–188, 1997). We provide an extension of the higher Specht basis to the generalized coinvariant ringsintroduced in Haglund et al. (Adv Math 329:851–915, 2018). We also give a conjectured higher Specht basis for the Garsia–Procesi modules, and we provide a proof of the conjecture in the case of two-row partition shapes. We then combine these results to give a higher Specht basis for an infinite subfamily of the modulesrecently defined by Griffin (Trans Amer Math Soc, to appear, 2020), which are a common generalization ofand.