Geometry of $q$-Hypergeometric Functions, Quantum Affine Algebras and Elliptic Quantum Groups
Geometry of $q$-Hypergeometric Functions, Quantum Affine Algebras and Elliptic Quantum Groups
The trigonometric quantized Knizhnik-Zamolodchikov equation (qKZ equation) associated with the quantum group $U_q(sl_2)$ is a system of linear difference equations with values in a tensor product of $U_q(sl_2)$ Verma modules. We solve the equation in terms of multidimensional $q$-hypergeometric functions and define a natural isomorphism between the space of solutions …