The modular double of a quantum group and hyperbolic hypergeometric integralsAlgebra & Discrete Mathematics
|Speaker:||Fokko van de Bult, University of Amsterdam|
|Start time:||Thu, May 18 2006, 12:10PM|
A quantum group is a deformation of the universal enveloping algebra of a Lie algebra. Basic hypergeometric functions naturally arise in the representation theory of these algebras. Hyperbolic hypergeometric functions are hypergeometric functions of a slightly different flavor than basic hypergeometric functions, due to the introduction of an extra parameter intimately related to q. The modular double of a quantum group is an extension of a quantum group incorporating a similar extra parameter. We will discuss how subsequently in the representation theory of the modular double of a quantum group hyperbolic hypergeometric functions naturally arise.