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1.
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 ,, three scalar parameters q,,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 , k . 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. 相似文献
2.
3.
We present several formulae for Selberg-type integrals associated with the Lie algebra
. 相似文献
4.
A. N. Varchenko 《Journal of Mathematical Sciences》1990,52(4):3305-3325
The paper presents a classification of typical singularities of the equilibrium surface and the phase diagram of a twocomponent themodynamic mixture. The mathematical formulation of the problem describes the evolutions of the convex hulls of plane curves dependent on two parameters. There is a total of eight topologicalfy different evolutions.Translated from Itogi Nauki i Tekhniki, Seriya Sovermennye Problemy Matematiki, Noveishie Dostizheniya, Vol. 33, pp. 157–190, 1988. 相似文献
5.
6.
The Ramanujan Journal - We construct polynomial solutions of the KZ differential equations over a finite field $${\mathbb F}_p$$ as analogs of hypergeometric solutions. 相似文献
7.
Apart from the Knizhnik-Zamolodchikov differential equations, correlation functions in Wess-Zumino-Witten models of conformal field theory satisfy a certain system of algebraic equations. We show that hypergeometric solutions of KZ equations constructed in [3] do satisfy these algebraic equations. 相似文献
8.
We consider the Knizhnik–Zamolodchikov (KZ) and dynamical equations, both differential and difference, in the context of (gl
k
,gl
n
) duality. We show that the KZ and dynamical equations naturally exchange under the duality. 相似文献
9.
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