ar X iv : h ep - t h / 93 05 08 4 v 2 1 2 Ju n 19 93 Representations of The Quantum Matrix Algebra
نویسنده
چکیده
It is shown that the finite dimensional irreducible representaions of the quantum matrix algebra Mq,p(2) ( the coordinate ring of GLq,p(2)) exist only when both q and p are roots of unity. In this case th e space of states has either the topology of a torus or a cylinder which may be thought of as generalizations of cyclic representations.
منابع مشابه
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 )
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 × ...
متن کاملX iv : h ep - t h / 93 05 08 6 v 2 1 2 Ju n 19 93 Q - BOSON REPRESENTATION OF THE QUANTUM MATRIX ALGEBRA
Although q-oscillators have been used extensively for realization of quantum universal enveloping algebras,such realization do not exist for quantum matrix algebras ( deformation of the algebra of functions on the group ). In this paper we first construct an infinite dimensional representation of the quantum matrix algebra Mq(3)(the coordinate ring of GLq(3)) and then use this representation to...
متن کاملar X iv : h ep - t h / 93 06 05 8 v 1 1 2 Ju n 19 93 Representations of The Coordinate Ring of GL
It is shown that the finite dimensional irreducible representations of the quantum matrix algebra Mq(n) ( the coordinate ring of GLq(n) ) exist only when q is a root of unity ( q = 1 ). The dimensions of these representations can only be one of the following values: p N 2 where N = n(n−1) 2 and k ∈ {0, 1, 2, ...N} For each k the topology of the space of states is (S1)×(N−k) × [0, 1](×(k) (i.e. ...
متن کاملar X iv : h ep - t h / 93 01 05 6 v 1 1 4 Ja n 19 93 QUANTUM GROUPS , CORRELATION FUNCTIONS AND INFRARED DIVERGENCES
We show in two simple examples that for one-dimensional quantum chains with quantum group symmetries, the correlation functions of local operators are, in general, infrared divergent. If one considers, however, correlation functions invariant under the quantum group, the divergences cancel out.
متن کاملar X iv : h ep - t h / 93 06 10 4 v 2 2 2 Ju n 19 93 IASSNS - HEP - 93 / 36 SPACE - TIME TRANSITIONS IN STRING THEORY ⋆
Simple mean field methods can be used to describe transitions between different space-time models in string theory. These include transitions between different Calabi-Yau manifolds, and more exotic things such as the Calabi-Yau/Landau-Ginzberg correspondence.
متن کامل