1. Q-Kostka polynomials and spin Green polynomials
- Author
-
Jiang, Anguo, Jing, Naihuan, and Liu, Ning
- Subjects
Mathematics - Quantum Algebra ,Mathematics - Combinatorics ,Primary: 05E05, Secondary: 17B69, 05E10 - Abstract
We study the $Q$-Kostka polynomials $L_{\lambda\mu}(t)$ by the vertex operator realization of the $Q$-Hall-Littlewood functions $G_{\lambda}(x;t)$ and derive new formulae for $L_{\lambda\mu}(t)$. In particular, we have established stability property for the Q-Kostka polynomials. We also introduce spin Green polynomials $Y^{\lambda}_{\mu}(t)$ 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 $Y^{\lambda}_{\mu}(t)$ are included for $n\leq7.$, Comment: 5 tables
- Published
- 2023
- Full Text
- View/download PDF