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  Suzuki functor at the critical level

Przeździecki, T. (2022). Suzuki functor at the critical level. Transformation Groups, 27(2), 659-722. doi:10.1007/s00031-020-09620-1.

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Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article,s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article,s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/ licenses/by/4.0/.

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Przeździecki, Tomasz1, Author           
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Representation Theory
 Abstract: In this paper we define and study a critical-level generalization of the Suzuki functor, relating the affine general linear Lie algebra to the rational Cherednik algebra of type A. Our main result states that this functor induces a surjective algebra homomorphism from the centre of the completed universal enveloping algebra at the critical level to the centre of the rational Cherednik algebra at t=0. We use this homomorphism to obtain several results about the functor. We compute it on Verma modules, Weyl modules, and their restricted versions. We describe the maps between endomorphism rings induced by the functor and deduce that every simple module over the rational Cherednik algebra lies in its image. Our homomorphism between the two centres gives rise to a closed embedding of the Calogero-Moser space into the space of opers on the punctured disc. We give a partial geometric description of this embedding.

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Language(s): eng - English
 Dates: 2022
 Publication Status: Published in print
 Pages: 64
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 Rev. Type: Peer
 Identifiers: arXiv: 1810.12226
DOI: 10.1007/s00031-020-09620-1
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Title: Transformation Groups
Source Genre: Journal
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Publ. Info: Birkhäuser
Pages: - Volume / Issue: 27 (2) Sequence Number: - Start / End Page: 659 - 722 Identifier: -