q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)

Details q-deformed KZB heat equation: completeness, modular properties and SL(3,Z) q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)

2001-10-08

arxiv.org/abs/math/0110081v1

Adv. Math. 171(2002)228-275

Mathematics

Quantum Algebra

39 pages

Scientific paper

10.1006/aima.2002.2080

We study the properties of one-dimensional hypergeometric integral solutions of the q-difference ("quantum") analogue of the Knizhnik-Zamolodchikov-Bernard equations on tori. We show that they also obey a difference KZB heat equation in the modular parameter, give formulae for modular transformations, and prove a completeness result, by showing that the associated Fourier transform is invertible. These results are based on SL(3,Z) transformation properties parallel to those of elliptic gamma functions.

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