Finite W-algebras for glN

De Sole, A., Kac, V. G. and Valeri, D. (2018) Finite W-algebras for glN. Advances in Mathematics, 327, pp. 173-224. (doi: 10.1016/j.aim.2017.06.016)

Abstract

We study the quantum finite W -algebras W (glN, f ), associ-ted to the Lie algebra glN, and its arbitrary nilpotent element f . We construct for such an algebra an r1× r1 matrix L(z) of Yangian type, where r1 is the number of maximal parts of the partition corresponding to f . The matrix L(z) is the quantum finite analogue of the operator of Adler type which we introduced in the classical affine setup. As in the latter case, the matrix L(z) is obtained as a generalized quasideterminant. It should encode the whole structure of W (glN, f ), including explicit formulas for generators and the commutation relations among them. We describe in all detail the examples of principal, rectangular and minimal nilpotent elements

• Item Type: Articles
• Additional Information: The first author is supported by National FIRB grant RBFR12RA9W, National PRIN grant 2012KNL88Y, and University grant C26A158K8A, the second author is supported by NSF grant DMS-1400967, and the third author is supported by NSFC “Research Fund for International Young Scientists” grant 11550110178.
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Valeri, Dr Daniele
• Authors: De Sole, A., Kac, V. G., and Valeri, D.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Advances in Mathematics
• Publisher: Elsevier
• ISSN: 0001-8708
• ISSN (Online): 1090-2082
• Published Online: 04 July 2017
• Copyright Holders: Copyright © 2017 Elsevier Inc.
• First Published: First published in Advances in Mathematics 327: 173-224
• Publisher Policy: Reproduced in accordance with the publisher copyright policy