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| Paper IPM / P / 6486 |
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| Abstract: | |
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It is shown that finite-dimensional irreducible representations of the quantum
matrix algebra Mq(3) (the coordinate ring of GLq(3)) exist only when q
is a root of unity (qp=1). The dimensions of these representations can only
be one of the following values: p3, p3/2, p3/4, or p3/8. The topology
of the space of states ranges between two extremes, from a three-dimensional
torus S1 ×S1 ×S1 (which may be thought of as a generalization
of the cyclic representation) to a
three-dimensional cube [0,1]×[0,1] ×[0,1].
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