0000000001180165
AUTHOR
Abdelkader Ben Hassine
Jeu de taquin and diamond cone for Lie (super)algebras
Abstract In this paper, we recall combinatorial basis for shape and reduced shape algebras of the Lie algebras gl ( n ) , sp ( 2 n ) and so ( 2 n + 1 ) . They are given by semistandard and quasistandard tableaux. Then we generalize these constructions to the case of the Lie superalgebra spo ( 2 n , 2 m + 1 ) . The main tool is an extension of Schutzenberger's jeu de taquin to these algebras.
Jeu de Taquin and Diamond Cone for so(2n+1, C)
International audience; 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 t…