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arXiv · 1504.04689

Twisted immanant and matrices with anticommuting entries

Minoru Itoh
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Abstract

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.

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Minoru Itoh. 2015-04-18. Twisted immanant and matrices with anticommuting entries. https://arxiv.org/abs/1504.04689

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