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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 2000-30
July 2000

Unitary Irreducible Representations of a Lie Algebra for Open Matrix Chains


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


We construct highest weight unitary irreducible representations of a Lie algebra for open quantum matrix chains akin to quotients of Verma modules for simple finite-dimensional Lie algebras. Those representations resembling typical unitary irreducible representations of $gl(n)$ turn out to be tensor products of the defining representation. They can be physically identified as multiple meson states or multiple open string states. Other representations are intimately related to the Cuntz algebra. They may be related to novel bound states.

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This paper has now been published in In " Theoretical high energy physics; MRST 2000". AIP Conference Proceedings 541, 130-139 (2000) New York