English

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

High Energy Physics - Theory 2009-10-22 v1 Quantum Algebra

Abstract

Highest weight representations of Uq(su(1,1))U_q(su(1,1)) with q=expπi/Nq=\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)Uq(su(2))SL(2,R)\otimes U_q(su(2)) is also presented in terms of holomorphic sections which also have Uq(su(2))U_q(su(2)) index. Furthermore we realise ZNZ_N-graded supersymmetry in terms of the representation. An explicit realization of Osp(12)Osp(1 \vert 2) via the heighest weight representation of Uq(su(1,1))U_q(su(1,1)) with q2=1q^2=-1 is given.

Keywords

Cite

@article{arxiv.hep-th/9312079,
  title  = {More on $U_q(su(1,1))$ with $q$ a Root of Unity},
  author = {Takashi Suzuki},
  journal= {arXiv preprint arXiv:hep-th/9312079},
  year   = {2009}
}

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24 pages