Séminaire Lotharingien de Combinatoire, 78B.25 (2017), 12 pp.
Jang Soo Kim, Kyu-Hwan Lee and Se-jin Oh
Dominant Maximal Weights of Highest Weight Modules and Young Tableaux
We study the multiplicities of dominant maximal weights of integrable
highest weight modules
V(Λ) with highest weights
Λ, including all fundamental weights, over affine Kac-Moody
algebras of types
We introduce new families of Young
tableaux, called the almost even tableaux and (spin) rigid tableaux,
and prove that they enumerate the crystal basis elements of dominant
maximal weight spaces. By applying inductive insertion schemes for
tableaux, in some special cases we prove that the weight
multiplicities of maximal weights form the Pascal, Motzkin, Riordan
and Bessel triangles.
Received: November 14, 2016.
Accepted: February 17, 2017.
Final version: April 1, 2017.
The following versions are available: