The exponential map for representations of $U_{p,q}(gl(2))$

Abstract

For the quantum group $G{L}_{p,q}(2)$ and the corresponding quantum algebra $U_{p,q}(gl(2))$ Fronsdal and Galindo explicitly constructed the so-called universal $T$-matrix. In a previous paper we showed how this universal $T$-matrix can be used to exponentiate representations from the quantum algebra to get representations (left comodules) for the quantum group. Here, further properties of the universal $T$-matrix are illustrated. In particular, it is shown how to obtain comodules of the quantum algebra by exponentiating modules of the quantum group. Also the relation with the universal $R$-matrix is discussed.

LaTeX-file, 7 pages. Submitted for the Proceedings of the 4th International Colloquium ``Quantum Groups and Integrable Systems,'' Prague, 22-24 June 1995

References in corpus (3)

• Free-Field Representation of Group Element for Simple Quantum Group
• Finite dimensional representations of the quantum group $G{L}_{p,q}(2)$ using the exponential map from $U_{p,q}(gl(2))$
• Exponential mapping for non semisimple quantum groups

Cited by in corpus (4)

• Dynamical actions and q-representation theory for double-scaled SYK
• Quantum exponentials for the modular double and applications in gravity models
• Universal T-matrix, Representations of OSp_q(1/2) and Little Q-Jacobi Polynomials
• The dual $(p,q)$-Alexander-Conway Hopf algebras and the associated universal $\mathcal{T}$-matrix