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arXiv · 2004.01889

Graded decompositions of fusion products in rank two

Leon Barth·Deniz Kus
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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.

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Leon Barth, Deniz Kus. 2020-04-04. Graded decompositions of fusion products in rank two. https://doi.org/10.1215/21562261-2022-0016

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