2,574 research outputs found
The dual -Alexander-Conway Hopf algebras and the associated universal -matrix
The dually conjugate Hopf algebras and associated
with the two-parametric -Alexander-Conway solution of the
Yang-Baxter equation are studied. Using the Hopf duality construction, the full
Hopf structure of the quasitriangular enveloping algebra is
extracted. The universal -matrix for is derived. While
expressing an arbitrary group element of the quantum group characterized by the
noncommuting parameters in a representation independent way, the -matrix generalizes the familiar exponential relation between a Lie group
and its Lie algebra. The universal -matrix and the FRT matrix
generators, , for are derived from the -matrix.Comment: LaTeX, 15 pages, to appear in Z. Phys. C: Particles and Field
Finite dimensional representations of the quantum group using the exponential map from
Using the Fronsdal-Galindo formula for the exponential mapping from the
quantum algebra to the quantum group , we show
how the -dimensional representations of can be obtained
by `exponentiating' the well-known -dimensional representations of
for ; 1/2 corresponds to the
defining 2-dimensional -matrix. The earlier results on the
finite-dimensional representations of and (or )
are obtained when . Representations of
\C \backslash \R and are also
considered. The structure of the Clebsch-Gordan matrix for is
studied. The same Clebsch-Gordan coefficients are applicable in the reduction
of the direct product representations of the quantum group .Comment: 17 pages, LaTeX (latex twice), no figures. Changes consist of more
general formula (4.13) for T-matrices, explicit Clebsch-Gordan coefficients,
boson realization of group parameters, and typographical correction
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