Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator
Quantum Algebra
2007-05-23 v3
Abstract
We consider the space of elliptic hypergeometric functions of the sl_2 type associated with elliptic curves with one marked point. This space represents conformal blocks in the sl_2 WZW model of CFT. The modular group acts on this space. We give formulas for the matrices of the action in terms of values at roots of unity of Macdonald polynomials of the sl_2 type.
Keywords
Cite
@article{arxiv.math/0203049,
title = {Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator},
author = {G. Felder and L. Stevens and A. Varchenko},
journal= {arXiv preprint arXiv:math/0203049},
year = {2007}
}
Comments
Latex, 19 pages; added remark in section 2 and remark in section 6, added references