论文信息 - Representations of two parameter quantum algebras and p,q-special functions

Representations of two parameter quantum algebras and p,q-special functions

Abstract In this paper, the connection between p , q -analogue of special functions and representations of certain two parameter quantum algebras has been developed. The realizations of the representations of these quantum algebras are in terms of p , q -derivative operators. The matrix elements of these representations are computed in terms of the generalized p , q -hypergeometric series. This leads to the developments in the theory of p , q -special functions.

Vivek Sahai | Sarasvati Yadav | Sarasvati Yadav | Vivek Sahai

[1] M. Nishizawa. U r,s ( gl 4 )-symmetry for ( r,s )-hypergeometric series , 2003 .

[2] Q-Algebra Representations Of The Euclidean, Pseudo-Euclidean And Oscillator Algebras, And Their Tens , 1994 .

[3] M. Takeuchi. A two-parameter quantization of ${GL}\left( n \right)$. (Summary) , 1990 .

[4] Willard Miller,et al. Lie Theory and Special Functions , 1969 .

[5] L. Vinet,et al. A note on (p, q)-oscillators and bibasic hypergeometric functions , 1993 .

[6] J. Jantzen. Lectures on quantum groups , 1995 .

[7] A. Klimyk,et al. P,Q-differentiation, P,Q-integration, and P,Q-hypergeometric functions related to quantum groups , 1994 .

[8] S. Srivastava,et al. On irreducible p, q -representations of gl(2) , 2003 .

[9] Ramaswamy Jagannathan,et al. A (p, q)-oscillator realization of two-parameter quantum algebras , 1991 .

[10] Mizan Rahman,et al. Basic Hypergeometric Series , 1990 .

[11] N. Vilenkin,et al. Representation of Lie groups and special functions , 1991 .