Representations of the Dynamical Affine Quantum Group $U_{q,x}(\widehat{sl_2})=U_{q,λ}(\widehat{sl_2})$ and Hypergeometric Functions

Bharath Narayanan

paper

Representations of the Dynamical Affine Quantum Group $U_{q, x} (s l_{2}) = U_{q, λ} (s l_{2})$ and Hypergeometric Functions

arXiv:1405.7853

Abstract

The representation theory of the Hopf algebroid $U_{q, x} (s l_{2}) = U_{q, λ} (s l_{2})$ is initiated and it is established that the intertwiner between the tensor products of dynamical evaluation modules is a well-poised balanced $_{10} W_{9}$ symbol, confirming a conjecture of Konno, that the degeneration of the elliptic $_{12} V_{11}$ series to $_{10} W_{9}$ can be proven based on the representation theory of $U_{q, x} (s l_{2})$ , the degeneration of the elliptic algebra $U_{q, p} (s l_{2})$ as $p \to 0$ .

arXiv comment38 pages, 2 figures. Misprints corrected and some improvements added

Representations of the Dynamical Affine Quantum Group Uq,x​(sl2​​)=Uq,λ​(sl2​​) and Hypergeometric Functions

Abstract

Representations of the Dynamical Affine Quantum Group $U_{q, x} (s l_{2}) = U_{q, λ} (s l_{2})$ and Hypergeometric Functions