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

Hjalmar Rosengren (Institutionen för matematiska vetenskaper, matematik)
Journal of Combinatorial Theory A Vol. 115 (2008), 3, p. 376-406.
[Artikel, refereegranskad vetenskaplig]

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.

Nyckelord: 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



Denna post skapades 2006-12-04. Senast ändrad 2014-09-29.
CPL Pubid: 23764

 

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Institutioner (Chalmers)

Institutionen för matematiska vetenskaper, matematik (2005-2016)

Ämnesområden

Matematik

Chalmers infrastruktur