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VOL. 76 | 2018 On the functor of Arakawa, Suzuki and Tsuchiya
Sergey Khoroshkin, Maxim Nazarov

Editor(s) Hitoshi Konno, Hidetaka Sakai, Junichi Shiraishi, Takao Suzuki, Yasuhiko Yamada

## Abstract

Arakawa, Suzuki and Tsuchiya defined a correspondence between certain modules of the trigonometric Cherednik algebra $\mathfrak{C}_N$ depending on a parameter $\kappa\in\mathbb{C}\,$, and certain modules of the affine Lie algebra $\widehat{\mathfrak{sl}}_m$ of level $\kappa-m\,$. We give a detailed proof of this correspondence by working with the affine Lie algebra $\widehat{\mathfrak{gl}}_m$ alongside of $\,\widehat{\mathfrak{sl}}_m\,$. We also relate this construction to a correspondence between certain modules of the degenerate affine Hecke algebra $\mathfrak{H}_N$ and all modules of $\mathfrak{sl}_m$ or $\mathfrak{gl}_m\,$. The latter correspondence was constructed earlier by Cherednik.

## Information

Published: 1 January 2018
First available in Project Euclid: 21 September 2018

zbMATH: 07039306
MathSciNet: MR3837925

Digital Object Identifier: 10.2969/aspm/07610275

Subjects:
Primary: 17B35