R Jagannathan and J Van der Jeugt 1995 J. Phys. A: Math. Gen. 28 2819 doi:10.1088/0305-4470/28/10/013
Finite-dimensional representations of the quantum group GLp,q(2) using the exponential map from Up,q(gl(2))
R Jagannathan and J Van der Jeugt
Show affiliationsUsing the Fronsdal-Galindo formula for the exponential mapping from the quantum algebra Up,q(gl(2)) to the quantum group GLp,q(2), we show how the (2j+1)-dimensional representations of GLp,q(2) can be obtained by 'exponentiating' the well known (2j+1)-dimensional representations of Up,q(gl(2)) for j=1, 3/2, ...; j= 1/2 corresponds to the defining two-dimensional T-matrix. The earlier results on the finite-dimensional representations of GLq(2) and SLq(2) (or SUq(2)) are obtained when p=q. Representations of Uq,q(2)(q in C mod R) and Uq(2)(q in R mod (0)) are also considered. The structure of the Clebsch-Gordan matrix for Up,q(gl(2)) is studied. The same Clebsch-Gordan coefficients are applicable in the reduction of the direct product representations of the quantum group GLp,q(2).
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Issue 10 (21 May 1995)
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Finite-dimensional representations of the quantum group GLp,q(2) using the exponential map from Up,q(gl(2))
R Jagannathan and J Van der Jeugt 1995 J. Phys. A: Math. Gen. 28 2819
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