Structure constants of diagonal reduction algebras of gl type

S. Khoroshkin (1) , O. Ogievetsky (2, 3)

1 BLTP - Bogoliubov Laboratory of Theoretical Physics [Dubna]
2 CPT - Centre de Physique Théorique - UMR 6207
3 CPT - Centre de Physique Théorique - UMR 7332

We describe, in terms of generators and relations, the reduction algebra, related to the diagonal embedding of the Lie algebra $\gl_n$ into $\gl_n\oplus\gl_n$. Its representation theory is related to the theory of decompositions of tensor products of $\gl_n$-modules.

Domaines: Anneaux et algèbres [math.RA]; Théorie des représentations [math.RT]; Physique mathématique [math-ph]; Physique mathématique [math-ph]

S. Khoroshkin, O. Ogievetsky. Structure constants of diagonal reduction algebras of gl type. Symmetry, Integrability and Geometry : Methods and Applications, 2011, 7, pp.064. ⟨10.3842/SIGMA.2011.064⟩. ⟨hal-00961353⟩