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Paper   IPM / P / 6485
School of Physics
  Title:   Representation of the Coordinatering of GLq(3)
  Author(s):  V. Karimipour
  Status:   Published
  Journal: Lett. Math. Phys.
  No.:  35
  Vol.:  28
  Year:  1993
  Pages:   207-217
  Supported by:  IPM
  Abstract:
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 ( 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 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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