Abstract
The diamond cone is a combinatorial description for a basis in a indecomposable module for the nilpotent factor n + of a semi-simple Lie algebra. After N.J. Wildberger who introduced this notion for sl ( 3 ) , this description was achevied in Arnal (2006) [2] for sl ( n ) and in Agrebaoui (2008) [1] for the rank 2 semi-simple Lie algebras. In the present work, we generalize these constructions to the Lie algebras sp ( 2 n ) . The symplectic semi-standard Young tableaux were defined by C. De Concini (1979) [4], they form a basis for the shape algebra of sp ( 2 n ) . We introduce here the notion of symplectic quasi-standard Young tableaux, these tableaux give the diamond cone for sp ( 2 n ) .
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
