Polynomial Realization of $s{\ell }_q(2)$ and Fusion Rules at Exceptional Values of $q$

Abstract

Representations of the $s{\ell }_q(2)$ algebra are constructed in the space of polynomials of real (complex) variable for $q^N=1$. The spin addition rule based on eigenvalues of Casimir operator is illustrated on few simplest cases and conjecture for general case is formulated.

References in corpus (1)

• Universal R operator with Jordanian deformation of conformal symmetry

Cited by in corpus (4)

• Intermediate-statistics spin waves
• Fusion Rules of the Lowest Weight Representations of osp_q(1|2) at Roots of Unity: Polynomial Realization and Degeneration at Roots of Unity
• New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity: cyclic representations
• New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity