Twisted immanant and matrices with anticommuting entries
Twisted immanant and matrices with anticommuting entries
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具有反交换项的扭曲固有矩阵和矩阵
DOI：
10.1080/03081087.2015.1112343
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发表时间：
2016
影响因子：
1.1
通讯作者：
伊藤稔
中科院分区：
文献类型：
--
作者：
Benoit Collins and Sho Matsumoto;石川雅雄;石川雅雄;伊藤稔
本文给出了一个新的矩阵函数“扭曲内变”，它可以看作是内变的类似物。这是通过对称群的不可约特征的“扭曲”模拟来定义每个自共轭划分的。这个扭曲的内在物有一些有趣的性质。例如，它满足柯西-比奈型公式。此外，它还与以下结果密切相关，这些结果是矩阵的条目彼此反交换的：(i)共轭下不变量的描述，以及（ii）对称多项式的柯西恒等式的模拟。
This article gives a new matrix function named ‘twisted immanant,’ which can be regarded as an analogue of the immanant. This is defined for each self-conjugate partition through a ‘twisted’ analogue of the irreducible character of the symmetric group. This twisted immanant has some interesting properties. For example, it satisfies Cauchy–Binet type formulas. Moreover it is closely related to the following results for matrices whose entries anticommute with each other: (i) the description of the invariants under the conjugations, and (ii) an analogue of the Cauchy identities for symmetric polynomials.