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

被引：8

作者：

Rosengren, Hjalmar ^{[1
,2
]}

机构：

[1] Chalmers, Dept Math Sci, SE-41296 Gothenburg, Sweden

[2] Univ Gothenburg, SE-41296 Gothenburg, Sweden

来源：

JOURNAL OF COMBINATORIAL THEORY SERIES A | 2008年 / 115卷 / 03期

关键词：

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;

D O I：

10.1016/j.jcta.2007.06.006

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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. (C) 2007 Elsevier Inc. All rights reserved.

引用

页码：376 / 406

页数：31

共 34 条

[1] [Anonymous], 1972, MEMOIRS AM MATH SOC
[2] [Anonymous], 1995, LINEAR MULTILINEAR A, DOI DOI 10.1080/03081089508818403
[3] [Anonymous], CONT MATH
[4] [Anonymous], 1998, ASKEY SCHEME HYPERGE
[5] [Anonymous], 1994, CONTEMP MATH
[6] SOME BASIC HYPERGEOMETRIC EXTENSIONS OF INTEGRALS OF SELBERG AND ANDREWS
ASKEY, R
[J]. SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1980, 11 (06) : 938 - 951
[7] On discrete q-ultraspherical polynomials and their duals
Atakishiyev, NM
Klimyk, AU
[J]. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2005, 306 (02) : 637 - 645
[8] Characteristic polynomials of random matrices
Brézin, E
Hikami, S
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2000, 214 (01) : 111 - 135
[9] de Bruijn N. G., 1955, J. Indian Math. Soc., V19, P133, DOI DOI 10.18311/JIMS/1955/17010.31
[10] THE HILLMAN-GRASSL CORRESPONDENCE AND THE ENUMERATION OF REVERSE PLANE PARTITIONS
GANSNER, ER
[J]. JOURNAL OF COMBINATORIAL THEORY SERIES A, 1981, 30 (01) : 71 - 89

← 1 2 3 4 →