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Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux |
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| Authors: | Hjalmar Rosengren |
| Institution: | Department of Mathematical Sciences, Chalmers University of Technology and Göteborg University, SE-412 96 Göteborg, Sweden |
| Abstract: | 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. |
| Keywords: | Schur Q-polynomial Marked shifted tableaux Pfaffian Multiple basic hypergeometric series Continuous q-ultraspherical polynomial Continuous q-Jacobi polynomial Askey-Wilson polynomial Christoffel-Darboux kernel Orthogonal polynomial ensemble Discrete Selberg integral Kawanaka's identity |
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