Multiple sine, multiple elliptic gamma functions and rational cones

Abstract

We define generalizations of the multiple elliptic gamma functions and the multiple sine functions, labelled by rational cones in ${\mathbb{R}}^r$. For $r=2,3$ we prove that the generalized multiple elliptic gamma functions enjoy a modular property determined by the cone. This generalizes the modular properties of the elliptic gamma function studied by Felder and Varchenko. The generalized multiple sine enjoy a related infinite product representation, generalizing the results of Narukawa for the ordinary multiple sine functions.

27 pages

References in corpus (6)

• SUSY Gauge Theories on Squashed Three-Spheres
• QKZ equation with |q|=1 and correlation functions of the XXZ model in the gapless regime
• The elliptic gamma function and SL(3,Z) x Z^3
• Superconformal Partition Functions and Non-perturbative Topological Strings
• q-deformed KZB heat equation: completeness, modular properties and SL(3,Z)
• The modular properties and the integral representations of the multiple elliptic gamma functions

Cited by in corpus (4)

• Holomorphic blocks and the 5d AGT correspondence
• N=2 supersymmetric gauge theory on connected sums of $S^2\times S^2$
• SYM on Quotients of Spheres and Complex Projective Spaces
• Mathematical structures behind supersymmetric dualities