MPS-RR 2000-30

July 2000

# Unitary Irreducible Representations of a Lie Algebra for Open Matrix Chains

by:

### 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
*