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Paper IPM / P / 6486  


Abstract:  
It is shown that finitedimensional irreducible representations of the quantum
matrix algebra M_{q}(3) (the coordinate ring of GL_{q}(3)) exist only when q
is a root of unity (q^{p}=1). The dimensions of these representations can only
be one of the following values: p^{3}, p^{3}/2, p^{3}/4, or p^{3}/8. The topology
of the space of states ranges between two extremes, from a threedimensional
torus S^{1} ×S^{1} ×S^{1} (which may be thought of as a generalization
of the cyclic representation) to a
threedimensional cube [0,1]×[0,1] ×[0,1].
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