Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator

Details Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator Modular transformations of the elliptic hypergeometric functions, Macdonald polynomials, and the shift operator

2002-03-06

arxiv.org/abs/math/0203049v3

Mathematics

Quantum Algebra

Latex, 19 pages; added remark in section 2 and remark in section 6, added references

Scientific paper

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.

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