Geodesic
Dominant Maximal Weights of Highest Weight Modules and Young Tableaux
Séminaire lotharingien de combinatoire, 78B (2017)

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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. 

@article{SLC_2017_78B_a24,
     author = {Jang Soo Kim and Kyu-Hwan Lee and Se-jin Oh},
     title = {Dominant {Maximal} {Weights} of {Highest} {Weight} {Modules} and {Young} {Tableaux}},
     journal = {S\'eminaire lotharingien de combinatoire},
     publisher = {mathdoc},
     volume = {78B},
     year = {2017},
     url = {http://geodesic.mathdoc.fr/item/SLC_2017_78B_a24/}
}
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%F SLC_2017_78B_a24
Jang Soo Kim; Kyu-Hwan Lee; Se-jin Oh. Dominant Maximal Weights of Highest Weight Modules and Young Tableaux. Séminaire lotharingien de combinatoire, 78B (2017). http://geodesic.mathdoc.fr/item/SLC_2017_78B_a24/