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

Giovanni Felder·Alexander Varchenko
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Abstract

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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Giovanni Felder, Alexander Varchenko. 2001-10-08. q-deformed KZB heat equation: completeness, modular properties and SL(3,Z). https://doi.org/10.1006/aima.2002.2080

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