Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux

Details Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux

2006-03-03

arxiv.org/abs/math/0603086v3

J. Combin. Theory A 115 (2008), 376-406

Mathematics

Combinatorics

34 pages; Appendix added, several minor improvements of previous version

Scientific paper

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.

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