Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 14 (2018), 053, 13 pages      arXiv:1803.01121      https://doi.org/10.3842/SIGMA.2018.053
Contribution to the Special Issue on the Representation Theory of the Symmetric Groups and Related Topics

A Spin Analogue of Kerov Polynomials

Sho Matsumoto
Graduate School of Science and Engineering, Kagoshima University, Kagoshima 890-0065, Japan

Received March 13, 2018, in final form May 29, 2018; Published online June 02, 2018

Abstract
Kerov polynomials describe normalized irreducible characters of the symmetric groups in terms of the free cumulants associated with Young diagrams. We suggest well-suited counterparts of the Kerov polynomials in spin (or projective) representation settings. We show that spin analogues of irreducible characters are polynomials in even free cumulants associated with double diagrams of strict partitions. Moreover, we present a conjecture for the positivity of their coefficients.

Key words: Kerov polynomials; spin symmetric groups; free cumulants; characters.

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