论文标题
杨的自然和半正态表示之间的过渡矩阵
Transition matrices between Young's natural and seminormal representations
论文作者
论文摘要
我们得出了杨对称组的半正态和自然表示之间的基础矩阵变化矩阵中条目的公式。这些条目被确定为标准tableaux上弱Bruhat图中加权路径的总和，我们表明可以将它们作为矩阵中最多两个先前计算的条目的加权总和进行递归计算。我们将结果推广到仿射Hecke代数，Ariki-Koike代数，Iwahori-Hecke代数以及由对称组有限循环组的花环产物给出的复杂反射组。
We derive a formula for the entries in the change-of-basis matrix between Young's seminormal and natural representations of the symmetric group. These entries are determined as sums over weighted paths in the weak Bruhat graph on standard tableaux, and we show that they can be computed recursively as the weighted sum of at most two previously-computed entries in the matrix. We generalize our results to work for affine Hecke algebras, Ariki-Koike algebras, Iwahori-Hecke algebras, and complex reflection groups given by the wreath product of a finite cyclic group with the symmetric group.
