Graded decompositions of fusion products in rank 2

摘要

We determine the graded decompositions of fusion products of finitedimensional irreducible representations for simple Lie algebras of rank 2. 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 parameterized by lattice points in convex polytopes, and an explicit hyperplane description is given in the various types.