BASIC HYPERGEOMETRIC-FUNCTIONS AND THE BOREL-WEIL CONSTRUCTION FOR U-Q(3)

被引：7

作者：

LOHE, MA ^{[1
]}

BIEDENHARN, LC ^{[1
]}

机构：

[1] NO TERR UNIV,CASUARINA,NT 0811,AUSTRALIA

来源：

SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 1994年 / 25卷 / 01期

关键词：

QUANTUM GROUP; BASIC HYPERGEOMETRIC FUNCTIONS; IRREDUCIBLE REPRESENTATIONS; BOREL-WELL CONSTRUCTION;

D O I：

10.1137/S0036141092226399

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The Borel-Weil construction of the irreducible unitary representations of the quantum group U-q(3) is investigated. The representation functions are calculated explicitly and found to be expressible in terms of basic hypergeometric functions; the form of these basis functions verifies previous general results. It is shown that several identities satisfied by basic hypergeometric functions, including a special case of Watson's formula, are implied by properties of the quantum group.

引用

页码：218 / 241

页数：24

共 50 条

[1] AN EXTENSION OF THE BOREL-WEIL CONSTRUCTION TO THE QUANTUM GROUP-U Q(N)
BIEDENHARN, LC
LOHE, MA
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 146 (03) : 483 - 504
[2] Bott-Borel-Weil construction for quantum supergroup U-q(gl(m vertical bar n))
Zhang, RB
JOURNAL OF MATHEMATICAL PHYSICS, 1997, 38 (07) : 3863 - 3884
[3] WEIL REPRESENTATION AND HYPERGEOMETRIC-FUNCTIONS ON LAGRANGIAN GRASSMANIANS
GONCHAROV, AB
DOKLADY AKADEMII NAUK SSSR, 1990, 312 (01): : 20 - 24
[4] PATH FUNCTIONS AND GENERALIZED BASIC HYPERGEOMETRIC-FUNCTIONS
KADELL, KWJ
MEMOIRS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 65 (360) : 1 - 54
[5] ON CERTAIN TRANSFORMATIONS OF BASIC HYPERGEOMETRIC-FUNCTIONS OF 3 VARIABLES
SAXENA, RK
GUPTA, RK
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1990, 21 (11): : 1009 - 1013
[6] Q-SERIES IDENTITIES AND REDUCIBILITY OF BASIC DOUBLE HYPERGEOMETRIC-FUNCTIONS
SRIVASTAVA, HM
JAIN, VK
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 1986, 38 (01): : 215 - 231
[7] ON CERTAIN Q-EXPANSIONS ASSOCIATED WITH MULTIVARIABLE BASIC HYPERGEOMETRIC-FUNCTIONS OF SRIVASTAVA
SAXENA, RK
GUPTA, RK
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1990, 21 (06): : 574 - 581
[8] CERTAIN EXPANSIONS ASSOCIATED WITH BASIC HYPERGEOMETRIC-FUNCTIONS OF 3 VARIABLES
KANDU, D
INDIAN JOURNAL OF PURE & APPLIED MATHEMATICS, 1988, 19 (06): : 562 - 566
[9] SOME TRANSFORMATIONS OF BASIC HYPERGEOMETRIC-FUNCTIONS .1.
VERMA, A
JAIN, VK
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1981, 12 (06) : 943 - 956
[10] GENERALIZED BASIC HYPERGEOMETRIC-FUNCTIONS AND THE Q-ANALOGS OF 3-J AND 6-J COEFFICIENTS
RAJESWARI, V
RAO, KS
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1991, 24 (16): : 3761 - 3780

← 1 2 3 4 5 →