Advanced Studies in Pure Mathematics

On the functor of Arakawa, Suzuki and Tsuchiya

Sergey Khoroshkin and Maxim Nazarov

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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

Source
Representation Theory, Special Functions and Painlevé Equations — RIMS 2015, H. Konno, H. Sakai, J. Shiraishi, T. Suzuki and Y. Yamada, eds. (Tokyo: Mathematical Society of Japan, 2018), 275-302

Dates
Received: 4 December 2015
Revised: 21 April 2016
First available in Project Euclid: 21 September 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1537499429

Digital Object Identifier
doi:10.2969/aspm/07610275

Mathematical Reviews number (MathSciNet)
MR3837925

Zentralblatt MATH identifier
07039306

Subjects
Primary: 17B35: Universal enveloping (super)algebras [See also 16S30]

Keywords
Affine Lie algebras Cherednik algebras

Citation

Khoroshkin, Sergey; Nazarov, Maxim. On the functor of Arakawa, Suzuki and Tsuchiya. Representation Theory, Special Functions and Painlevé Equations — RIMS 2015, 275--302, Mathematical Society of Japan, Tokyo, Japan, 2018. doi:10.2969/aspm/07610275. https://projecteuclid.org/euclid.aspm/1537499429


Export citation