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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.