Jeu de Taquin and Diamond Cone for so(2n+1, C) - Archive ouverte HAL
Article Dans Une Revue Journal of Lie Theory Année : 2020

Jeu de Taquin and Diamond Cone for so(2n+1, C)

Résumé

The diamond cone is a combinatorial description for a basis of a natural indecomposable n-module, where n is the nilpotent factor of a complex semisimple Lie algebra g. After N. J. Wildberger who introduced this notion, this description was achieved for g = sl(n) , the rank 2 semisimple Lie algebras and g = sp (2n). In this work, we generalize these constructions to the Lie algebra g = so(2n + 1). The orthogonal semistandard Young tableaux were defined by M. Kashiwara and T. Nakashima, they index a basis for the shape algebra of so(2n + 1). Defining the notion of orthogonal quasistandard Young tableaux, we prove that these tableaux describe a basis for a quotient of the shape algebra, the reduced shape algebra of so(2n + 1).
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Dates et versions

hal-03058376 , version 1 (11-12-2020)

Identifiants

  • HAL Id : hal-03058376 , version 1

Citer

Boujemaa Agrebaoui, Didier Arnal, Abdelkader Ben Hassine. Jeu de Taquin and Diamond Cone for so(2n+1, C). Journal of Lie Theory, 2020, 30 (1), pp.277-303. ⟨hal-03058376⟩
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