Representations of The Coordinate Ring of $GL_{q}(3)$

Details Representations of The Coordinate Ring of $GL_{q}(3)$ Representations of The Coordinate Ring of $GL_{q}(3)$

1993-05-19

arxiv.org/abs/hep-th/9305085v2

J.Phys. A26 (1993) L957-L962

Physics

High Energy Physics

High Energy Physics - Theory

pages 20

Scientific paper

10.1007/BF00745152

It is shown that the finite dimensional ireducible 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 \over 2 } , { p^3 \over 4 } $ or $ { p^3 \over 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 ] $ .

Affiliated with

Also associated with

No associations

Rating

Representations of The Coordinate Ring of $GL_{q}(3)$ does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Representations of The Coordinate Ring of $GL_{q}(3)$, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Representations of The Coordinate Ring of $GL_{q}(3)$ will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-222342