On the functor of Arakawa, Suzuki and Tsuchiya

Abstract

Arakawa, Suzuki and Tsuchiya constructed 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.

22 pages

References in corpus (1)

• A generalized Harish-Chandra isomorphism