2002/07/18 by Pavel Etingof, Olivier Schiffmann, Etingof, Pavel +3
Mathematics · #Advanced Algebra and Geometry #Advanced Operator Algebra Research #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA
paper · pdf · doi:10.48550/arxiv.math/0207157
19 pages, latex
arxiv created 2002/07/18 · openalex publication_date 2002/07/18 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study twisted traces of products of intertwining operators for quantum affine algebras. They are interesting special functions, depending on two weights lambda, mu, three scalar parameters q, omega, k, and spectral parameters z1,...,zN, which may be regarded as q-analogs of conformal blocks of the Wess-Zumino-Witten model on an elliptic curve. It is expected that in the rank 1 case they essentially coincide with the elliptic hypergeometric functions defined in math.QA/0110081. Our main result is that after a suitable renormalization the traces satisfy four systems of difference equations -- the Macdonald-Ruijsenaars equation, the q-Knizhnik-Zamolodchikov-Bernard equation, and their dual versions. We also show that in the case when the twisting automorphism is trivial, the trace functions are symmetric under the permutation lambda mu, k omega. Thus, our results here generalize our previous results, dealing with the case q = 1 and the finite dimensional case.