A Lax type operator for quantum finite W-algebras
Name
1707.03669.pdf
Description
Accepted version
Size
432.78 KB
Format
Adobe PDF
Checksum (MD5)
3ecbcb60b9207145cb26e062b3372b25
Author(s)
De Sole, Alberto
Kac, Victor G
Valeri, Daniele
Date Issued
2018
Journal
Selecta Mathematica, New Series
Publisher
Springer Science and Business Media LLC
Version
Author's final manuscript
Abstract
© 2018, Springer Nature Switzerland AG. 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.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
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Creative Commons Attribution-Noncommercial-Share Alike
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DOI of Published Version
https://doi.org/10.1007/S00029-018-0439-6
