Weight Multiplicities and Young Tableaux Through Affine Crystals - Kim, Jang Soo; Lee, Kyu-Hwan; Oh, Se-jin (Memoirs of the American Mathematical Society, 2023)
The weight multiplicities of finite dimensional simple Lie algebras can be computed individually using various methods. Still, it is hard to derive explicit closed formulas. Similarly, explicit closed formulas for the multiplicities of maximal weights of affine Kac–Moody algebras are not known in most cases. In this paper, we study weight multiplicities for both finite and affine cases of classical types for certain infinite families of highest weights modules. We introduce new classes of Young tableaux, called the