6533b821fe1ef96bd127b652

RESEARCH PRODUCT

Jeu de taquin and diamond cone for Lie (super)algebras

Boujemaâ AgrebaouiDidier ArnalAbdelkader Ben Hassine

subject

Pure mathematicsGeneral MathematicsLie algebraJeu de taquinLie superalgebraBasis (universal algebra)Cone (category theory)Extension (predicate logic)Mathematics

description

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.

yearjournalcountryeditionlanguage
2015-02-01Bulletin des Sciences Mathématiques
https://doi.org/10.1016/j.bulsci.2014.08.004