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

Abstract

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