Representations of The Coordinate Ring of $G{L}_q(3)$

Abstract

It is shown that the finite dimensional ireducible representations of the quantum matrix algebra $M_q(3)$ ( the coordinate ring of $G{L}_q(3)$ ) 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: $p^3,\frac{p^3}{2},\frac{p^3}{4}$ or $\frac{p^3}{8}$ . The topology of the space of states ranges between two extremes , from a 3-dimensional torus $S^1\times S^1\times S^1$ ( which may be thought of as a generalization of the cyclic representation ) to a 3-dimensional cube $[0,1]\times [0,1]\times [0,1]$ .

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Cited by in corpus (1)

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