A Lax type operator for quantum finite W-algebras

De Sole, A., Kac, V. G. and Valeri, D. (2018) A Lax type operator for quantum finite W-algebras. Selecta Mathematica - New Series, 24(5), pp. 4617-4657. (doi: 10.1007/s00029-018-0439-6)

Abstract

For a reductive Lie algebra g , its nilpotent element f and its faithful finite dimensional representation, we construct a Lax operator L(z) with coefficients in the quantum finite W-algebra W(g,f) . We show that for the classical linear Lie algebras glN , slN , soN and spN , the operator L(z) satisfies a generalized Yangian identity. The operator L(z) is a quantum finite analogue of the operator of generalized Adler type which we recently introduced in the classical affine setup. As in the latter case, L(z) is obtained as a generalized quasideterminant.

• Item Type: Articles
• Additional Information: The first author is supported by National FIRB Grant RBFR12RA9W, National PRIN Grant 2015ZWST2C, and University Grant C26A158K8A, the second author was supported by an NSF grant.
• 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: Selecta Mathematica - New Series
• Publisher: Springer
• ISSN: 1022-1824
• ISSN (Online): 1420-9020
• Published Online: 14 September 2018
• Copyright Holders: Copyright © 2018 Springer Nature Switzerland AG
• First Published: First published in Selecta Mathematica - New Series 24:4617–4657
• Publisher Policy: Reproduced in accordance with the publisher copyright policy