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arXiv · 2304.07439

Q-Kostka polynomials and spin Green polynomials

Anguo Jiang·Naihuan Jing·Ning Liu
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Abstract

We study the $Q$-Kostka polynomials $L_{λμ}(t)$ by the vertex operator realization of the $Q$-Hall-Littlewood functions $G_λ(x;t)$ and derive new formulae for $L_{λμ}(t)$. In particular, we have established stability property for the Q-Kostka polynomials. We also introduce spin Green polynomials $Y^λ_μ(t)$ as both an analogue of the Green polynomials and deformation of the spin irreducible characters of $\mathfrak S_n$. Iterative formulas of the spin Green polynomials are given and some favorable properties parallel to the Green polynomials are obtained. Tables of $Y^λ_μ(t)$ are included for $n\leq7.$

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BibTeXRIS

Anguo Jiang, Naihuan Jing, Ning Liu. 2023-04-15. Q-Kostka polynomials and spin Green polynomials. https://doi.org/10.1007/s00605-023-01843-0

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