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

Abstract

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 $Osp(1|2)$ via the heighest weight representation of $U_q(su(1,1))$ with $q^2=-1$ is given.

24 pages

References in corpus (2)

• Exactly Solvable Potentials and Quantum Algebras
• Paragrassmann Analysis and Quantum Groups

Cited by in corpus (1)

• A Note on Quantum Liouville Theory via Quantum Group; an Approach to Strong Coupling Liouville Theory