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Centre for Mathematical Physics and Stochastics
Department of Mathematical Sciences, University of Aarhus

Funded by The Danish National Research Foundation

MPS-RR 2000-43
November 2000

Unitary Irreducible Representations of a Lie Algebra for Matrix Chain Models


H.P. Jacobsen, C.-W. H. Lee


There is a decomposition of a Lie algebra for open matrix chains akin to the triangular decompostion. 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.

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This paper has now been published in J. Math. Phys. 42, 3817--3838 (2001)