On \(sl(n)\)-modules of finite-dimensional weight
type: Item
instance of: scholarly article
title: On \(sl(n)\)-modules of finite-dimensional weight
zbMATH Open document ID: 0799.17006
DOI: 10.1007/BF01077066
author: B. V. Lidskij
publication date: 1994-04-12T00:00:00Z
review text: The author describes a set of representations of \(sl(n)\) on certain subspaces of the infinite-dimensional complex space with the canonical basis \(\alpha(m)\) where \(m\) runs over all elements of the lattice \(\mathbb{Z}^{n(n-1)/2}\). It is then stated that for any indecomposable scalar representation \(\rho\) of \(sl(n)\) (\(n\neq 3\)) of finite-dimensional weight and any \(\nu\in {\mathfrak h}^*\) (\({\mathfrak h}\) the Cartan subalgebra consisting of diagonal matrices in \(sl(n)\)) there exists a representation \(\tau\) in this set such that \(\rho\) and \(\tau\) are isomorphic in the weight \(\nu\).
Mathematics Subject Classification ID: 17B10
zbMATH DE Number: 525652
zbMATH Keywords: representations of \(sl(n)\)
zbMATH Keywords: Cartan subalgebra
MaRDI profile type: Publication
cites work: Remarks on the perturbation theory for problems of Mathieu type
cites work: Three coupled oscillators: Mode-locking, global bifurcations and toroidal chaos
cites work: Resonance regions for Mathieu type dynamical systems on a torus
cites work: Resonance regions for families of torus maps
full work available at URL: https://doi.org/10.1007/bf01077066
OpenAlex ID: W1976765258
published in: Functional Analysis and Its Applications
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description: scientific article; zbMATH DE number 525652