Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux
Copyright policy )Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux
We study Schur Q-polynomials evaluated on a geometric progression, or equivalently q-enumeration of marked shifted tableaux, seeking explicit formulas that remain regular at q=1. We obtain several such expressions as multiple basic hypergeometric series, and as determinants and pfaffians of continuous q-ultraspherical or continuous q-Jacobi polynomials. As special cases, we obtain simple closed formulas for staircase-type partitions.
34 pages; Appendix added, several minor improvements of previous version
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Schur \(Q\)-polynomial, Continuous q-Jacobi polynomial, Theoretical Computer Science, Christoffel-Darboux kernel, Askey-Wilson polynomial, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Askey–Wilson polynomial, Kawanaka's identity, Marked shifted tableaux, Discrete Selberg integral, continuous \(q\)-ultraspherical polynomial, continuous \(q\)-Jacobi polynomial, discrete Selberg integral, Pfaffian, marked shifted tableaux, multiple basic hypergeometric series, 05E05, 05E10, 33D52, orthogonal polynomial ensemble, Computational Theory and Mathematics, Mathematics - Classical Analysis and ODEs, Combinatorial aspects of representation theory, Schur Q-polynomial, Orthogonal polynomial ensemble, Christoffel–Darboux kernel, Combinatorics (math.CO), Multiple basic hypergeometric series, Continuous q-ultraspherical polynomial
Basic orthogonal polynomials and functions (Askey-Wilson polynomials, etc.), Schur \(Q\)-polynomial, Continuous q-Jacobi polynomial, Theoretical Computer Science, Christoffel-Darboux kernel, Askey-Wilson polynomial, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Discrete Mathematics and Combinatorics, Mathematics - Combinatorics, Askey–Wilson polynomial, Kawanaka's identity, Marked shifted tableaux, Discrete Selberg integral, continuous \(q\)-ultraspherical polynomial, continuous \(q\)-Jacobi polynomial, discrete Selberg integral, Pfaffian, marked shifted tableaux, multiple basic hypergeometric series, 05E05, 05E10, 33D52, orthogonal polynomial ensemble, Computational Theory and Mathematics, Mathematics - Classical Analysis and ODEs, Combinatorial aspects of representation theory, Schur Q-polynomial, Orthogonal polynomial ensemble, Christoffel–Darboux kernel, Combinatorics (math.CO), Multiple basic hypergeometric series, Continuous q-ultraspherical polynomial
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