English

Graded decompositions of fusion products in rank two

Representation Theory 2023-02-22 v1 Rings and Algebras

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.

Keywords

Cite

@article{arxiv.2004.01889,
  title  = {Graded decompositions of fusion products in rank two},
  author = {Leon Barth and Deniz Kus},
  journal= {arXiv preprint arXiv:2004.01889},
  year   = {2023}
}