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[en] In this article, imposing Hermitian conjugate relations on the two-parameter deformed quantum group GLp,q(2) is studied. This results in a noncommutative phase associated with the unitarization of the quantum group. After the achievement of the quantum group Up,q(2) with pq real via a noncommutative phase, the representation of the algebra is built by means of the action of the operators constituting the Up,q(2) matrix on states
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