More on $U_q(su(1,1))$ with $q$ a Root of Unity

Details More on $U_q(su(1,1))$ with $q$ a Root of Unity More on $U_q(su(1,1))$ with $q$ a Root of Unity

1993-12-10

arxiv.org/abs/hep-th/9312079v1

J.Math.Phys. 35 (1994) 6857-6874

Physics

High Energy Physics

High Energy Physics - Theory

24 pages

Scientific paper

10.1063/1.530646

Highest weight representations of $U_q(su(1,1))$ with $q=\exp \pi i/N$ are investigated. The structures of the irreducible hieghesat weight modules are discussed in detail. The Clebsch-Gordan decomposition for the tensor product of two irreducible representations is discussed. By using the results, a representation of $SL(2,R)\otimes U_q(su(2))$ is also presented in terms of holomorphic sections which also have $U_q(su(2))$ index. Furthermore we realise $Z_N$-graded supersymmetry in terms of the representation. An explicit realization of $Osp(1 \vert 2)$ via the heighest weight representation of $U_q(su(1,1))$ with $q^2=-1$ is given.

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