Gelfand-Tsetlin-type weight bases for all special linear Lie algebra representations corresponding to skew Schur functions
DOI10.1016/j.aam.2022.102356OpenAlexW3115276222WikidataQ115362372 ScholiaQ115362372MaRDI QIDQ2672950
Molly Dunkum, Donnelly, Robert G.
Publication date: 13 June 2022
Published in: Advances in Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2012.14986
distributive latticemodular latticeSchur functionskew Schur functionsemisimple Lie algebra representationskew-shaped semistandard tableauskew-tabular latticeskew-tabular parallelogramsplitting posetweight basis supporting graph / representation diagramWeyl bialternantWeyl symmetric function
Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Unimodular groups, congruence subgroups (group-theoretic aspects) (20H05) Reflection and Coxeter groups (group-theoretic aspects) (20F55) Combinatorial aspects of groups and algebras (05E16)
Related Items
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Solution of a Sperner conjecture of Stanley with a construction of Gelfand
- Alcove walks, Hecke algebras, spherical functions, crystals and column strict tableaux.
- Constructions of representations of rank two semisimple Lie algebras with distributive lattices
- Geometry of G/P. V
- A new interpretation of Gelfand-Tsetlin bases
- A generalization of the Littlewood-Richardson rule and the Robinson- Schensted-Knuth correspondence
- Finite-dimensional representations of the quantum superalgebra \(U_ q[gl(n/m)\) and related \(q\)-identities]
- Extremal properties of bases for representations of semisimple Lie algebras
- Constructions of representations of \(\text{o}(2n+1,{\mathbb C})\) that imply Molev and Reiner-Stanton lattices are strongly Sperner
- Principal Galois orders and Gelfand-Zeitlin modules
- Gelfand-Tsetlin bases of representations for super Yangian and quantum affine superalgebra
- Gelfand-Tsetlin theory for rational Galois algebras
- Bruhat lattices, plane partition generating functions, and minuscule representations
- Combinatorial constructions of weight bases: the Gelfand-Tsetlin basis
- Solitary and edge-minimal bases for representations of the simple Lie algebra \(G_2\)
- Multiplicity-free skew Schur polynomials
- Gelfand–Tsetlin Bases for Classical Lie Algebras
- Extremal Bases for the Adjoint Representations of the Simple Lie Algebras
- Representations of $\mathfrak{sl}( 2,\mathbb{C} )$ on Posets and the Sperner Property
- Weight bases of Gelfand-Tsetlin type for representations of classical Lie algebras
- WEIGHT MULTIPLICITY FREE REPRESENTATIONS, ${\frak g}$-ENDOMORPHISM ALGEBRAS, AND DYNKIN POLYNOMIALS
- Combinatorial bases for covariant representations of the Lie superalgebra gl(m|n)
- Distributive Lattices Defined for Representations of Rank Two Semisimple Lie Algebras
- Gel’fand–Zetlin basis and Clebsch–Gordan coefficients for covariant representations of the Lie superalgebra gl(m∣n)
- Towards a combinatorial classification of skew Schur functions
- Introduction to Lie Algebras and Representation Theory
- Explicit constructions of the fundamental representations of the symplectic Lie algebras
- A concise proof of the Littlewood-Richardson rule
- Gelfand-Tsetlin polytopes and the integer decomposition property
