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A Howe correspondence for the algebra of the $\mathfrak{osp}(1|2)$ Clebsch-Gordan coefficients

Quantum Algebra 2020-08-26 v1 Mathematical Physics math.MP

Abstract

Two descriptions of the dual 1-1 Hahn algebra are presented and shown to be related under Howe duality. The dual pair involved is formed by the Lie algebra o(4)\mathfrak{o}(4) and the Lie superalgebra osp(12)\mathfrak{osp}(1|2).

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Cite

@article{arxiv.2004.00109,
  title  = {A Howe correspondence for the algebra of the $\mathfrak{osp}(1|2)$ Clebsch-Gordan coefficients},
  author = {Julien Gaboriaud and Luc Vinet},
  journal= {arXiv preprint arXiv:2004.00109},
  year   = {2020}
}

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12 pages