# 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} }

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)

- Mathematics
- 2016

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)

- Mathematics
- 2016

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…

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