Some remarks on the construction of quantum symmetric spaces

被引：27

作者：

Dijkhuizen, MS ^{[1
]}

机构：

[1] KOBE UNIV, FAC SCI, DEPT MATH, KOBE 657, JAPAN

来源：

ACTA APPLICANDAE MATHEMATICAE | 1996年 / 44卷 / 1-2期

关键词：

compact quantum group; quantum symmetric space; quantum projective space; zonal spherical function; two-sided coideal; Casimir operator; radial part; Askey-Wilson polynomials; Macdonald's symmetric polynomials; Koornwinder's BC-type Askey-Wilson polynomials;

D O I：

10.1007/BF00116516

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We present a general survey of some recent developments regarding the construction of compact quantum symmetric spaces and the analysis of their zonal spherical functions in terms of q-orthogonal polynomials. In particular, we define a one-parameter family of two-sided coideals in U-q(gl(n, C)) and express the zonal spherical functions on the corresponding quantum projective spaces as Askey-Wilson polynomials containing two continuous and one discrete parameter.

引用

页码：59 / 80

页数：22

共 39 条

[1]

ANDREWS GE, 1985, LECT NOTES MATH, V1171, P36

[2]

[Anonymous], 1990, ENCY MATH ITS APPL

[3]

ASKEY R, 1985, MEM AM MATH SOC, V54, P1

[4]

CHIN W, CORADICAL FILTRATION

[5] CQG ALGEBRAS - A DIRECT ALGEBRAIC APPROACH TO COMPACT QUANTUM GROUPS [J].

DIJKHUIZEN, MS ;

KOORNWINDER, TH .

LETTERS IN MATHEMATICAL PHYSICS, 1994, 32 (04) :315-330

[6] QUANTUM HOMOGENEOUS SPACES, DUALITY AND QUANTUM 2-SPHERES [J].

DIJKHUIZEN, MS ;

KOORNWINDER, TH .

GEOMETRIAE DEDICATA, 1994, 52 (03) :291-315

[7]

DIJKHUIZEN MS, 1996, FAMILY QUANTUM PROJE

[8]

Drinfel'd V. G., 1987, P INT C MATHEMATICIA, V1, P798

[9]

HAYASHI T, 1992, TOKYO J MATH, V15, P431, DOI DOI 10.3836/TJM/1270129467

[10]

HECKMAN GJ, 1995, PERSPECTIVES MATH, V16

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