Symplecton for U H (sl(2)) and Representations of Sl H (2)
نویسنده
چکیده
Polynomials of boson creation and annihilation operators which form irreducible tensor operators for Jordanian quantum algebra U h (sl(2)), called h-symplecton, are introduced and their properties are investigated. It is shown that many properties of symplecton for Lie algebra sl(2) are extended to h-symplecton. The h-symplecton is also a basis of irreducible representation of SL h (2) dual to U h (sl(2)). As an application of the procedure used to construct h-symplecton, we construct the representation bases of SL h (2) on the quantum h-plane.
منابع مشابه
2 7 Ju n 20 05 A two - parametric deformation of U [ sl ( 2 ) ] , its representations and complex ” spin ”
A two-parametric deformation of U [sl(2)], its representations and complex " spin " Abstract A two-parametric deformation of U [sl(2)] and its representations are considered. This newly introduced two-parametric quantum group denoted as U pq [sl(2)] admits a class of infinite-dimensional representations which have no classical (non-deformed) and one-parametric deformation analogues, even at gen...
متن کاملep - t h / 02 02 12 1 v 1 1 9 Fe b 20 02 Hamiltonian Quantization of Chern - Simons theory with SL ( 2 , C )
We analyze the hamiltonian quantization of Chern-Simons theory associated to the real group SL(2, C) R , universal covering of the Lorentz group SO(3, 1). The algebra of observables is generated by finite dimensional spin networks drawn on a punctured topological surface. Our main result is a construction of a unitary representation of this algebra. For this purpose we use the formalism of comb...
متن کاملRepresentations of SL(2)×G
Let g be a complex reductive Lie algebra. We investigate a formalism for producing a natural model for representations of sl(2) × g which decompose in such a way so as to produce interesting correspondences between representations of sl(2) and of g. Our formalism generalizes the standard dual pair SL(2)× O(2n). We use it to obtain a formally unitary representation of sl(2,R)×u(3) that essential...
متن کاملTHE HARISH-CHANDRA ISOMORPHISM FOR sl(2,C)
Given a reductive Lie algebra g and choice of Cartan subalgebra h, the HarishChandra map gives an isomorphism between the center z of the universal enveloping algebra U(g) of g and the algebra of Weyl group invariant symmetric tensors of h, denoted S(h) . We define these objects and give a sketch of the proof, using sl(2,C) as a motivating example. The proofs and examples mirror those found in ...
متن کاملTensor Operators for U H (sl(2))
Tensor operators for the Jordanian quantum algebra U h (sl(2)) are considered. Some explicit examples of them, which are obtained in the boson or fermion realization , are given and their properties are studied. It is also shown that the Wigner-Eckart's theorem can be extended to U h (sl(2)).
متن کامل