1Université de Sfax, Faculté des Sciences, Dép. de Mathématiques, 3000 Sfax, Tunisie 2Université de Bourgogne-Franche Comté, Institut de Mathématiques, U.F.R. Sciences et Techniques, 21078 Dijon, France 3University of Bisha, Dept. of Mathematics, Faculty of Science and Arts, Belqarn, Sabt Al-Alaya 61985, Kingdom of Saudi Arabia
Journal of Lie Theory, Tome 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).
1
Université de Sfax, Faculté des Sciences, Dép. de Mathématiques, 3000 Sfax, Tunisie
2
Université de Bourgogne-Franche Comté, Institut de Mathématiques, U.F.R. Sciences et Techniques, 21078 Dijon, France
3
University of Bisha, Dept. of Mathematics, Faculty of Science and Arts, Belqarn, Sabt Al-Alaya 61985, Kingdom of Saudi Arabia
Boujemaâ Agrebaoui; Didier Arnal; Abdelkader Ben Hassine. Jeu de Taquin and Diamond Cone for so(2n+1, C). Journal of Lie Theory, Tome 30 (2020) no. 1, pp. 277-303. http://geodesic.mathdoc.fr/item/JOLT_2020_30_1_a15/
@article{JOLT_2020_30_1_a15,
author = {Boujema\^a Agrebaoui and Didier Arnal and Abdelkader 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},
url = {http://geodesic.mathdoc.fr/item/JOLT_2020_30_1_a15/}
}
TY - JOUR
AU - Boujemaâ Agrebaoui
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AU - Abdelkader Ben Hassine
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JO - Journal of Lie Theory
PY - 2020
SP - 277
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