QUANTUM ALGEBRAS AND Q-SPECIAL FUNCTIONS

被引:61
作者
FLOREANINI, R
VINET, L
机构
[1] UNIV MONTREAL,PHYS NUCL LAB,MONTREAL H3C 3J7,QUEBEC,CANADA
[2] UNIV MONTREAL,CTR RECH MATH,MONTREAL H3C 3J7,QUEBEC,CANADA
关键词
D O I
10.1006/aphy.1993.1003
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
A quantum-algebraic framework for many q-special functions is provided. The two-dimensional Euclidean quantum algebra, slq(2) and the q-oscillator algebra are considered. Realizations of these algebras in terms of operators acting on vector spaces of functions in one complex variable are given. Basic hypergeometric functions are shown to arise, in analogy with Lie theory, as matrix elements of certain operators. New generating functions for these q-special functions are obtained. © 1993 Academic Press. All rights reserved.
引用
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页码:53 / 70
页数:18
相关论文
共 42 条
[1]   CANONICAL EQUATIONS AND SYMMETRY TECHNIQUES FOR Q-SERIES [J].
AGARWAL, AK ;
KALNINS, EG ;
MILLER, W .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1987, 18 (06) :1519-1538
[2]  
Andrews GE., 1977, HIGHER COMBINATORICS, P3, DOI [10.1007/978-94-010-1220-1_1, DOI 10.1007/978-94-010-1220-1_1]
[3]   THE QUANTUM GROUP SUQ(2) AND A Q-ANALOGUE OF THE BOSON OPERATORS [J].
BIEDENHARN, LC .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1989, 22 (18) :L873-L878
[4]   SOME POLYNOMIALS RELATED TO THETA FUNCTIONS [J].
CARLITZ, L .
DUKE MATHEMATICAL JOURNAL, 1957, 24 (04) :521-527
[5]  
Carlitz L., 1956, ANN MAT PURA APPL, V41, P359, DOI DOI 10.1007/BF02411676
[6]  
Chihara T.S., 1978, INTRO ORTHOGONAL POL
[7]  
Drinfel'd V. G., 1987, P INT C MATH BERKELE, V1, P798
[8]  
Erdelyi A, 1953, HIGHER TRANSCENDENTA
[9]  
Faddeev L.D., 1988, ALGEBRAIC ANAL, VI, P129
[10]   THE METAPLECTIC REPRESENTATION OF SUQ(1,1) AND THE Q-GEGENBAUER POLYNOMIALS [J].
FLOREANINI, R ;
VINET, L .
JOURNAL OF MATHEMATICAL PHYSICS, 1992, 33 (04) :1358-1362