Certer-Payne定理的某些$q$ -类似
Some $q$-analogues of the Certer-Payne theorem
摘要：
我们证明了一个$q$ -类似的卡特-佩恩定理的两种特殊情况下，相应的移动任意数量的节点之间的相邻行，或移动一个节点之间的任意数量的行。作为结果，我们表明，这些同态空间是一维时，$q \neq -1$。我们应用这些结果完成了对称群的Hecke代数的可约Specht模的分类，当$q \neq-1$。我们的方法也可以用来确定某些其他对的Specht模块之间有一个同态。特别地，我们描述了从平凡模到任意Specht模的同态空间。
英文摘要：
We prove a $q$-analogue of the Carter-Payne theorem for the two special cases corresponding to moving an arbitrary number of nodes between adjacent rows, or moving one node between an arbitrary number of rows. As a consequence, we show that these homomorphism spaces are one dimensional when $q \neq -1$. We apply these results to complete the classification of the reducible Specht modules for the Hecke algebras of the symmetric groups when $q \neq-1$. Our methods can also be used to determine certain other pairs of Specht modules between which there is a homomorphism. In particular, we describe the homomorphism space from the trivial module to an arbitrary Specht module.
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