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 \(n\le 7.\)
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Acknowledgements
The project is partially supported by Simons Foundation Grant No. 523868 and NSFC Grant No. 12171303.
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Communicated by Ilse Fischer.
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Jiang, A., Jing, N. & Liu, N. Q-Kostka polynomials and spin Green polynomials. Monatsh Math 201, 109–125 (2023). https://doi.org/10.1007/s00605-023-01843-0
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DOI: https://doi.org/10.1007/s00605-023-01843-0