# Traces of Intertwiners for Quantum Affine $${\mathfrak{sl}}_2$$sl2 and Felder–Varchenko Functions

@article{Sun2016TracesOI,
title={Traces of Intertwiners for Quantum Affine \$\$\{\mathfrak\{sl\}\}\_2\$\$sl2 and Felder–Varchenko Functions},
author={Yi Sui Sun},
journal={Communications in Mathematical Physics},
year={2016},
volume={347},
pages={573-653}
}
• Y. Sun
• Published 17 August 2015
• Mathematics
• Communications in Mathematical Physics
AbstractWe show that the traces of $${U_q({\widehat{\mathfrak{sl}}}_2)}$$Uq(sl^2)-intertwiners of [ESV02] valued in the three-dimensional evaluation representation converge in a certain region of parameters and give a representation-theoretic construction of Felder–Varchenko’s hypergeometric solutions to the q-KZB heat equation given in [FV02]. This gives the first proof that such a trace function converges and resolves the first case of the Etingof–Varchenko conjecture of [EV00]. As…
3 Citations
TRACES OF INTERTWINERS FOR QUANTUM AFFINE ALGEBRAS AND DIFFERENCE EQUATIONS (AFTER ETINGOF–SCHIFFMANN–VARCHENKO)
We modify and give complete proofs for the results of Etingof–Schiffmann–Varchenko in [ESV02] on traces of intertwiners of untwisted quantum affine algebras in the opposite coproduct and the standard
Affine Macdonald conjectures and special values of Felder–Varchenko functions
• Mathematics
• 2016
We refine the statement of the denominator and evaluation conjectures for affine Macdonald polynomials proposed by Etingof–Kirillov Jr. (Duke Math J 78(2):229–256, 1995) and prove the first
TRACES OF INTERTWINERS FOR QUANTUM AFFINE ALGEBRAS AND DIFFERENCE EQUATIONS (AFTER ETINGOF-SCHIFFMANN-VARCHENKO)
We modify and give complete proofs for the results of Etingof-Schiffmann-Varchenko in [ESV02] on traces of intertwiners of untwisted quantum affine algebras in the opposite coproduct and the standard

## References

SHOWING 1-10 OF 34 REFERENCES
BRST Cohomology in Quantum Affine Algebra $U_q(\widehat{sl_2})$
Using free field representation of quantum affine algebra $U_q(\widehat{sl_2})$, we investigate the structure of the Fock modules over $U_q(\widehat{sl_2})$. The analisys is based on a $q$-analog of
Aq-deformation of Wakimoto modules, primary fields and screening operators
AbstractTheq-vertex operators of Frenkel and Reshetikhin are studied by means of aq-deformation of the Wakimoto module for the quantum affine algebraUq $$(\widehat{\mathfrak{s}\mathfrak{l}}_2 )$$ at
Representations of affine Lie algebras, parabolic differential equations, and Lamé functions
• Mathematics
• 1993
We consider correlation functions for the Wess-Zumino-Witten model on the torus with the insertion of a Cartan element; mathematically this means that we consider the function of the form $F=\Tr Quantum affine Gelfand–Tsetlin bases and quantum toroidal algebra via K-theory of affine Laumon spaces Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GLn. We construct the action of the quantum loop algebra$\${U_v({\bf
Traces of Intertwiners for Quantum Groups and Difference Equations
• Mathematics
• 2000
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
Algebraic Integrability of Macdonald Operators and Representations of Quantum Groups
• Mathematics
Compositio Mathematica
• 1998
In this paper we construct examples of commutative rings of difference operators with matrix coefficients from representation theory of quantum groups, generalizing the results of our previous paper
Laumon spaces and the Calogero-Sutherland integrable system
AbstractThis paper contains a proof of a conjecture of Braverman concerning Laumon quasiflag spaces. We consider the generating function Z(m), whose coefficients are the integrals of the equivariant
Resonance relations, holomorphic trace functions and hypergeometric solutions to qKZB and Macdonald-Ruijsenaars equations
• Mathematics
• 2006
The resonance relations are identities between coordinates of functions with values in tensor products of representations of the quantum group Uq(sl2). We show that the space of hypergeometric