Graded decompositions of fusion products in rank two

Abstract

We determine the graded decompositions of fusion products of finite-dimensional irreducible representations for simple Lie algebras of rank two. Moreover, we give generators and relations for these representations and obtain as a consequence that the Schur positivity conjecture holds in this case. The graded Littlewood-Richardson coefficients in the decomposition are parametrized by lattice points in convex polytopes and an explicit hyperplane description is given in the various types.

References in corpus (3)

• Fusion products and toroidal algebras
• Weyl modules for the hyperspecial current algebra
• Twisted Demazure modules, fusion product decomposition and twisted Q--systems