q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)
q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)
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q 变形 KZB 热方程：完整性、模属性和 SL(3,Z)
DOI：
10.1006/aima.2002.2080
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发表时间：
2001
影响因子：
1.7
通讯作者：
A. Varchenko
中科院分区：
文献类型：
--
作者：
G. Felder;A. Varchenko
摘要研究了环面上Knizhnik-Zamolodchikov-Bernard方程的q-差(量子)模拟的一维超几何积分解的性质。通过证明相应的傅里叶变换是可逆的，我们证明了它们在模参数上也服从一个差KZB热方程，给出了模变换的公式，并证明了一个完备性结果。这些结果是基于与椭圆伽玛函数平行的SL(3，Z)变换性质的。
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.