Fusion rules and [formula omitted]-matrix for the composition of regular spins with semi-periodic representations of SL(2) q

• Published in: Physics letters. B 1991-10, Vol.268 (2), p.217-221
• Main Author: Arnaudon, Daniel
• Format: Article
• Language: English
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/0370-2693(91)90806-2

We perform the composition, when the parameter q is an mth root of unity, of the spin j representation of SL(2) q with semi-periodic representations characterized by two complex parameters. The result is proved to be completely reducible and it is a direct sum of semi-periodic representations. Denoting by “indecomposable spin representations” the indecomposable representations arising from composition of spin j and spin j' representations, we also prove that the tensor product of indecomposable spin representations with semi-periodic representations is a direct sum of semi-periodic representations. So the set of highest weight representations including spin j representations (1 ⩽ 2 j + 1 ⩽ m), indecomposable spin representations and semi-periodic representations is closed under tensor product. R - matrices which intertwine the tensor products of spin 1 2 representation with semi-periodic representations are derived. These R -matrices satisfy three Yang-Baxter equations.