论文标题
规范基础以及增加和减少不变理论的新应用
Canonical bases and new applications of increasing and decreasing subsequences to invariant theory
论文作者
论文摘要
2012年，拉加万（Raghavan），塞缪尔（Samuel）和Subrahmanyam表明，A型iWahori-hecke代数的kazhdan-lusztig基础为Schur代数的Centermiser代数提供了``规范性的''基础。在2022年，第二作者发现了作用于相同张量空间的分区代数的中央框架的类似结果。每个基础都由排列索引。我们利用这些基础来表明，任意不变的（在Centeriser代数中）的线性分解取决于其条目，并描述了挑选最小条目集的组合规则。
In 2012 Raghavan, Samuel, and Subrahmanyam showed that the Kazhdan--Lusztig basis for the Iwahori--Hecke algebra in type A provides a ``canonical'' basis for the centraliser algebra of the Schur algebra acting on tensor space. In 2022 the second author found a similar result for the centraliser of the partition algebra acting on the same tensor space. Each basis is indexed by permutations. We exploit these bases to show that the linear decomposition of an arbitrary invariant (in either centraliser algebra) depends integrally on its entries, and describe combinatorial rules that pick out minimal sets of such entries.
