Abstract
Let L denote a finite-dimensional, simple Lie algebra over the complex numbers C and fix a Cart an subalgebra H. An C- module V is said to be Ti-diagonalizable if \( \mathcal{V} = \oplus \sum {_{\mu \in \mathcal{H}*} } \mathcal{V}_\mu where \mathcal{V}_\mu = \left\{ {v \in \mathcal{V}|hv = \mu (h)v for all h \in \mathcal{H}} \right\} \). Further V is said to have bounded multiplicities provided there exists a constant B such that dim Vμ ≤ B for all μ ∈ H*. The minimum such bound is said to be the degree of the module.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
G.M. Benkart, D.J. Britten, and F.W. Lemire, Modules with bounded weight multiplicities for simple Lie algebras, Math. Z. 225 (1997), no. 2, 333–353.
D.J. Britten, V. Futorny, and F.W. Lemire, Simple A2 modules with a finite-dimensional weight space, Comm. Algebra 23 (1995), 467–510.
D.J. Britten, J. Hooper, and F.W. Lemire, Simple C n -modules with multiplicities 1 and applications, Canad. J. Phys. 72 (1994), 326–335.
D.J. Britten and F. W. Lemire, On modules of bounded multiplicities for the symplectic algebra, Trans. Amer. Math. Soc. 351 (1999), no. 8, 3413–3431.
D.J. Britten and F.W. Lemire, A Pieri-like formula for torsion-free modules, preprint.
L. Chen, Simple torsion-free C 2 -rfiodules having finite-dimensional weight spaces, Master’s thesis, University of Windsor, 1995.
S.L. Fernando, Lie algebra modules with finite-dimensional weight spaces I, Trans. Amer. Math. Soc. 322 (1990), 757–781.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer Science+Business Media New York
About this chapter
Cite this chapter
Britten, D.J., Lemire, F.W. (2001). Lie Modules of Bounded Multiplicities. In: Saint-Aubin, Y., Vinet, L. (eds) Algebraic Methods in Physics. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-0119-6_3
Download citation
DOI: https://doi.org/10.1007/978-1-4613-0119-6_3
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6528-3
Online ISBN: 978-1-4613-0119-6
eBook Packages: Springer Book Archive