Explicit constructions of the fundamental representations of the symplectic Lie algebras

DOI10.1006/jabr.2000.8446zbMath0971.17003OpenAlexW2069504257WikidataQ115395762 ScholiaQ115395762MaRDI QIDQ5925792

Donnelly, Robert G.

Publication date: 31 October 2001

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jabr.2000.8446

zbMATH Keywords

fundamental representationssymplectic Lie algebra

Mathematics Subject Classification ID

Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (6)

Gelfand-Tsetlin-type weight bases for all special linear Lie algebra representations corresponding to skew Schur functions ⋮ Extremal properties of bases for representations of semisimple Lie algebras ⋮ The symplectic diamond cone ⋮ Gelfand–Tsetlin Bases for Classical Lie Algebras ⋮ Symplectic analogs of the distributive lattices \(L(m,n)\) ⋮ Extremal Bases for the Adjoint Representations of the Simple Lie Algebras

Cites Work

• Solution of a Sperner conjecture of Stanley with a construction of Gelfand
• Symplectic standard tableaux
• A basis for representations of symplectic Lie algebras
• Young tableaux, Gelfand patterns, and branching rules for classical groups
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Yangians and Gelfand-Zetlin bases
• Unimodality of differences of specialized Schur functions
• Symplectic analogs of the distributive lattices \(L(m,n)\)
• Bruhat lattices, plane partition generating functions, and minuscule representations
• Construction of Sp-modules by tableaux
• Representations of $\mathfrak{sl}( 2,\mathbb{C} )$ on Posets and the Sperner Property
• Weyl Groups, the Hard Lefschetz Theorem, and the Sperner Property
• Construction of orthogonal group modules using tableaux
• A symplectic jeu de taquin bijection between the tableaux of King and of De Concini
• Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras
• Solution of Two Difficult Combinatorial Problems with Linear Algebra
• Introduction to Lie Algebras and Representation Theory
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