2015/04/18 by Itoh, Minoru
#05E05 #15A24 #15A75 #15B33 #20C30 #FOS: Mathematics #Primary 15A15 #Representation Theory (math.RT) #Secondary 16R
paper · doi:10.48550/arxiv.1504.04689
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.