English

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