Abstract
A q-analogue of the root system is constructed for this algebra which is similar to the root system of classical Lie algebras. It is then used to construct, in detail, a class of representations of the algebra of functions on the quantum group GLq(n), and a q-boson realization of the generators of GLq(n) is given. I also construct infinite-dimensional Hilbert-space representations of this algebra. The main result of this paper is stated in proposition 8.
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