Representations of the quantum matrix algebra $M_{q,p}(2)$

Abstract

It is shown that the finite dimensional irreducible representaions of the quantum matrix algebra $M_{q,p}(2)$ ( the coordinate ring of $G{L}_{q,p}(2)$) 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.

20 pages

Cited by in corpus (2)

• Quantum Chains with $G{L}_q(2)$ Symmetry
• Integrable Spin Chains Associated to $\widehat{s{l}_q(n)}$ and $\widehat{s{l}_{p,q}(n)}$