NDLI: Traces of Intertwiners for Quantum Groups and Difference Equations

Content Provider	Springer Nature Link
Author	Etingof, P. Schiffmann, O. Varchenko, A.
Copyright Year	2002
Abstract	In this Letter we study twisted traces of products of intertwining operators for quantum affine algebras. They are interesting special functions, depending on two weights λ,μ, three scalar parameters q,ω,k, and spectral parameters z $_{1}$,...,z $_{ N }$, 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 by Felder and Varchenko. 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 λ ↔ μ, k ↔ ω. Thus, our results generalize those of Etingof and Schiffmann, dealing with the case q=1, and Etingof, Varchenko, and Schiffmann, dealing with the finite-dimensional case.
Starting Page	143
Ending Page	158
Page Count	16
File Format	PDF
ISSN	03779017
Journal	Letters in Mathematical Physics
Volume Number	62
Issue Number	2
e-ISSN	15730530
Language	English
Publisher	Kluwer Academic Publishers
Publisher Date	2002-01-01
Publisher Place	Dordrecht
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Group Theory and Generalizations Geometry Mathematical and Computational Physics Statistical Physics
Content Type	Text
Resource Type	Article
Subject	Statistical and Nonlinear Physics Mathematical Physics

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