Explicit constructions of the fundamental representations of the symplectic Lie algebras
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Publication:5925792
DOI10.1006/jabr.2000.8446zbMath0971.17003OpenAlexW2069504257WikidataQ115395762 ScholiaQ115395762MaRDI QIDQ5925792
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
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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