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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

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Using 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).


PACS

02.20.Uw Quantum groups

02.10.Yn Matrix theory

MSC

20G42 Quantum groups (quantized function algebras) and their representations (See also 16W35, 17B37, 81R50)

16W30 Coalgebras, bialgebras, Hopf algebras (See also 16S40, 57T05); rings, modules, etc. on which these act

Subjects

Mathematical physics

Dates

Issue 10 (21 May 1995)



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