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

Abstract. 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 B(1)n, D(1)n, A(2)2n-1, A(2)2n and D(2)n+1. 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.

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