2025/01/27 by Biswal, Rekha, Gaussent, Stéphane
#FOS: Mathematics #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2501.15837
In this paper, using crystal theory we prove the existence of a new family of irreducible components appearing in the tensor product of two irreducible integrable highest weight modules over symmetrizable Kac-Moody algebras motivated by the Schur positivity conjecture, Kostant conjecture and Wahl conjecture. We also prove Schur positivity conjecture in full generality when the Lie algebra is a simple Lie algebra under the assumption that λ> > μ, i.e. if λ and μ are the two dominant weights appearing in the tensor product then λ+wμ is a dominant weight for all the Weyl group elements w.