✦ LIBER ✦
Q-Deformed KZB Heat Equation: Completeness, Modular Properties and SL(3, Z)
✍ Scribed by Giovanni Felder; Alexander Varchenko
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 377 KB
- Volume
- 171
- Category
- Article
- ISSN
- 0001-8708
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✦ Synopsis
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 SLð3; ZÞ transformation properties parallel to those of elliptic gamma functions.