(math-ph): Unitary Irreducible Representations of a Lie Algebra for Matrix Chain...

[Chi-Wei Herbert Lee]

Title: Unitary Irreducible Representations of a Lie Algebra for Matrix Chain
Models

Author(s): H. P. Jakobsen, C.-W. H. Lee

There is a decomposition of a Lie algebra for open matrix chains akin to the
triangular decomposition. We use this decomposition to construct unitary
irreducible representations. All multiple meson states can be retrieved this
way. Moreover, they are the only states with a finite number of non-zero
quantum numbers with respect to a certain set of maximally commuting linearly
independent quantum observables. Any other state is a tensor product of a
multiple meson state and a state coming from a representation of a quotient
algebra that extends and generalizes the Virasoro algebra. We expect the
representation theory of this quotient algebra to describe physical systems at
the thermodynamic limit.

Paper: math-ph/0011002
Dated: Wed, 1 Nov 2000 08:54:35 GMT (26kb)
Comments: 46 pages, no figure, LaTeX2e, amssymb, latexsym
Report-no: MPS-RR 2000-43
Subj-class: Mathematical Physics; Representation Theory
MSC-class: 17B65

URL: http://arXiv.org/abs/math-ph/0011002