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### The modular double of a quantum group and hyperbolic hypergeometric integrals

**Algebra & Discrete Mathematics**

Speaker: | Fokko van de Bult, University of Amsterdam |

Location: | 1147 MSB |

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.