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Transition matrices for symmetric and quasisymmetric Hall-Littlewood polynomials. (English) Zbl 1278.05241
Summary: We introduce explicit combinatorial interpretations for the coefficients in some of the transition matrices relating to skew Hall-Littlewood polynomials \(P_{{\lambda}/{\mu}}(t)\) and Hivert’s quasisymmetric Hall-Littlewood polynomials \(G_{\gamma}(t)\). More specifically, we provide: 0.5 cm
the \(G\)-expansions of the Hall-Littlewood polynomials \(P_\lambda(t)\), the monomial quasisymmetric polynomials \(M_{\alpha}\), the quasisymmetric Schur polynomials \(S_{\alpha}\), and the peak quasisymmetric functions \(K_{\alpha}\);
an expansion of \(P_{{\lambda}/{\mu}}(t)\) in terms of the \(F_{\alpha}\)’s.
The \(F\)-expansion of \(P_{{\lambda}/{\mu}}(t)\) is facilitated by introducing starred tableaux.

05E05 Symmetric functions and generalizations
05E10 Combinatorial aspects of representation theory
Full Text: DOI arXiv
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