Quantum deformation of Whittaker modules and the Toda lattice.
type: Item
instance of: scholarly article
title: Quantum deformation of Whittaker modules and the Toda lattice.
zbMATH Open document ID: 1058.17009
DOI: 10.1215/S0012-7094-00-10522-4
author: Alexey Sevostyanov
published in: Duke Mathematical Journal
publication date: 2002-10-27T00:00:00Z
full work available at URL: https://arxiv.org/abs/math/9905128
review text: Let \(\mathfrak{g}\) be a complex simple finite-dimensional Lie algebra. It this very interesting paper the author constructs a quantum analogue of the Whittaker model of the center of \(U(\mathfrak{g})\), which was introduced in the classical case by \textit{B. Kostant} in [Invent. Math. 48, 101--184 (1978; Zbl 0405.22013)]. As the positive part of the the quantum group \(U_h(\mathfrak{g})\) does not have nonsingular characters, the author uses a new realization of the quantum groups, developed by him in \textit{A. Sevostyanov} [Commun. Math. Phys. 204, No. 1, 1--16 (1999; Zbl 0955.17011)]. Using the Whittaker model of the center of \(U_h(\mathfrak{g})\), the author introduces quantum deformations of Whittaker modules and studies the deformed quantum Toda lattice.
reviewed by: Volodymyr Mazorchuk
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 16T20
zbMATH DE Number: 1820761
zbMATH Keywords: Whittaker module
zbMATH Keywords: Toda lattice
zbMATH Keywords: quantum group
MaRDI profile type: Publication
arXiv ID: math/9905128
cites work: Q4846800
cites work: Q4065692
cites work: Q5749435
cites work: Q4952803
cites work: Q3202270
cites work: Q4040877
cites work: Universal \(R\)-matrix for quantized (super)algebras
cites work: Lie Group Representations on Polynomial Rings
cites work: On Whittaker vectors and representation theory
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OpenAlex ID: W1997482588
description: scientific article