Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux
Journal article, 2008

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.

Pfaffian

Orthogonal polynomial ensemble

Askey–Wilson polynomial

Multiple basic hypergeometric series

Continuous q-Jacobi polynomial

Discrete Selberg integral

Kawanaka's identity

Marked shifted tableaux

Continuous q-ultraspherical polynomial

Christoffel–Darboux kernel

Schur Q-polynomial

Author

Hjalmar Rosengren

Chalmers, Mathematical Sciences, Mathematics

University of Gothenburg

Journal of Combinatorial Theory - Series A

0097-3165 (ISSN)

Vol. 115 3 376-406

Subject Categories

Mathematics

DOI

10.1016/j.jcta.2007.06.006

More information

Created

10/7/2017