X 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
نویسنده
چکیده
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 realize GLq(3) by q-bosons.
منابع مشابه
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
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.
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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 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. ...
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We show that any covariant scattering amplitude of the W 3 string will contain, as part of its integrand, a factor that obeys the differential equations satisfied by an Ising model correlation function. This factor can thus be identified with such a correlation function, in agreement with a previous result of the authors. The W 3 string is also shown to contain an N = 2 parafermion theory, and ...
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