Representations and Q-Boson Realization of the Algebra of Functions on the Quantum Group GLq(N)

Abstract

We present a detailed study of the representations of the algebra of functions on the quantum group $G{L}_q(n)$. A q-analouge of the root system is constructed for this algebra which is then used to determine explicit matrix representations of the generators of this algebra. At the end a q-boson realization of the generators of $G{L}_q(n)$ is given.

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