Duality for KnizhnikZamolodchikov and Dynamical Equations, and Hypergeometric Integrals
Abstract
We review results on the KnizhnikZamolodchikov (KZ) and dynamical equations, both differential and difference, in the context of the $(gl_k,gl_n)$ duality, and their implications for hypergeometric integrals. The KZ and dynamical equations naturally exchange under the duality, which provides two kinds of integral formulae for hypergeometric solutions of the equations. This fact yields identities for hypergeometric integrals of different dimensions, the dimension of the first integral being the parameter of the second one, and vice versa. Similar identites exist between hypergeometric and qhypergeometric integrals of MellinBarnes type of different dimensions. Those identites are multidimensional analogues of the equality of two integral representations for the Gauss hypergeometric function.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2004
 arXiv:
 arXiv:math/0401245
 Bibcode:
 2004math......1245T
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Mathematics  Representation Theory
 EPrint:
 Preprint, 29 pages, AmsLaTeX, to appear in Proceedings of IDAQUIS, (Infinite Dimensional Algebras and Quantum Integrable Systems), Faro, Portugal, July 2125, 2003