Journal of Lie Theory

no. 1
Jeu de Taquin and Diamond Cone for so(2n+1, C)
Journal of Lie Theory, Volume 30 (2020) no. 1, pp. 277-303
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).
DOI: 10.5802/jolt.1115
Classification: 20G05, 05A15, 17B10
Keywords: Shape algebra, semistandard Young tableau, quasistandard Young tableau, jeu de taquin 
@article{JOLT_2020_30_1_a15,
     author = {B. Agrebaoui and D. Arnal and A. Ben Hassine},
     title = {Jeu de {Taquin} and {Diamond} {Cone} for so(2n+1, {C)}},
     journal = {Journal of Lie Theory},
     pages = {277--303},
     year = {2020},
     volume = {30},
     number = {1},
     doi = {10.5802/jolt.1115},
     zbl = {1459.17013},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1115/}
}
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B. Agrebaoui; D. Arnal; A. Ben Hassine. Jeu de Taquin and Diamond Cone for so(2n+1, C). Journal of Lie Theory, Volume 30 (2020) no. 1, pp. 277-303. doi: 10.5802/jolt.1115

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