## Advanced Studies in Pure Mathematics

### On the functor of Arakawa, Suzuki and Tsuchiya

#### 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.

#### Article information

Dates
Revised: 21 April 2016
First available in Project Euclid: 21 September 2018

https://projecteuclid.org/ euclid.aspm/1537499429

Digital Object Identifier
doi:10.2969/aspm/07610275

Mathematical Reviews number (MathSciNet)
MR3837925

Zentralblatt MATH identifier
07039306

Subjects