Construction of Sp-modules by tableaux

DOI10.1080/03081088608817725zbMath0601.22009OpenAlexW2091212699MaRDI QIDQ3735967

Allan Berele

Publication date: 1986

Published in: Linear and Multilinear Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/03081088608817725

zbMATH Keywords

Specht modulessymplectic groupsYoung tableauxsemi-standard tableauxGarnir relationsSp-standard tableaux

Mathematics Subject Classification ID

Representations of finite symmetric groups (20C30) Semisimple Lie groups and their representations (22E46)

Related Items

Representations of symplectic groups and the symplectic tableaux of R. C. King, A Generalized Berele-Schensted Algorithm and Conjectured Young Tableaux for Intermediate Symplectic Groups, Toward a conjecture of Pappas and Rapoport on a scheme attached to the symplectic group, Construction of GL(n)modules using composite tableaux, Unimodality of differences of specialized Schur functions, On induced modules and tableaux for the special orthogonal groups, A note on the straightening law for the symplectic group, Construction of orthogonal group modules using tableaux, Distributive lattices, affine semigroups, and branching rules of the classical groups, A Basis of Bideterminants for the Coordinate Ring of the Orthogonal Group, A bideterminant basis for a reductive monoid, The nullcone in the multi-vector representation of the symplectic group and related combinatorics, A symplectic Désarménien matrix and a standard basis for the symplectic Weyl module., Standard monomial theory for flag algebras of GL\((n)\)and Sp\((2n)\), Explicit constructions of the fundamental representations of the symplectic Lie algebras, Construction of graded covariant \(GL(m/n)\) modules using tableaux, Hibi algebras and representation theory, Gelfand–Tsetlin Bases for Classical Lie Algebras, Matrices with involution and invariant theory, Symplectic analogs of the distributive lattices \(L(m,n)\), Identities from representation theory, On odd symplectic Schur functions

Cites Work

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• The evaluation of weight multiplicities using characters and S-function
• Kronecker products for compact semisimple Lie groups
• Standard Young tableaux and weight multiplicities of the classical Lie groups