ar X iv : h ep - t h / 93 05 08 5 v 2 1 2 Ju n 19 93 Representations of The Coordinate Ring of GL q ( 3 )
نویسنده
چکیده
It is shown that the finite dimensional ireducible representations of the quantum matrix algebra Mq(3) ( the coordinate ring of GLq(3) ) exist only when q is a root of unity ( q = 1 ). The dimensions of these representations can only be one of the following values: p3 , p 3 2 , p 4 , or p 8 . The topology of the space of states ranges between two extremes , from a 3-dimensional torus S1 × S1 × S1 ( which may be thought of as a generalization of the cyclic representation ) to a 3-dimensional cube [0, 1] × [0, 1] × [0, 1] .
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