Schur Q-polynomials, multiple hypergeometric series and enumeration of marked shifted tableaux
Artikel i vetenskaplig tidskrift, 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
Författare
Hjalmar Rosengren
Chalmers, Matematiska vetenskaper, Matematik
Göteborgs universitet
Journal of Combinatorial Theory - Series A
0097-3165 (ISSN) 10960899 (eISSN)
Vol. 115 3 376-406Ämneskategorier
Matematik
DOI
10.1016/j.jcta.2007.06.006