Young tableaux and crystal \(\mathcal B(\infty)\) for finite simple Lie algebras

DOI10.1016/j.jalgebra.2008.06.008zbMath1218.17007arXivmath/0507448OpenAlexW1999014353WikidataQ112881509 ScholiaQ112881509MaRDI QIDQ958990

Hyeonmi Lee, Jin Hong

Publication date: 10 December 2008

Published in: Journal of Algebra, Algebras and Representation Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0507448

zbMATH Keywords

Young tableaucrystal basecrystalmarginally large tableaufinite simple Lie algebrasemi-standard tableauclassical simple Lie algebra

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10) Representations of Lie algebras and Lie superalgebras, algebraic theory (weights) (17B10) Quantum groups (quantized enveloping algebras) and related deformations (17B37)

Related Items (35)

Virtual crystals and Nakajima monomials ⋮ Connecting marginally large tableaux and rigged configurations via crystals ⋮ The \(\mathcal{B}(\infty)\) crystal for a family of generalized quantum groups ⋮ PBW bases and marginally large tableaux in types B and C ⋮ Lusztig data of Kashiwara-Nakashima tableaux in types \(B\) and \(C\) ⋮ Extended Nakajima monomials and crystal \({\mathcal B}(\infty)\) for finite simple Lie algebras ⋮ Rigged configurations and the \(\ast\)-involution ⋮ Realizations of crystal \(\mathcal B(\infty)\) using Young tableaux and Young walls ⋮ Description of \(\mathsf {B}(\infty)\) through Kashiwara embedding for Lie algebra types \(E_6\) and \(E_7\) ⋮ A crystal embedding into Lusztig data of type \(A\) ⋮ Candidate for the crystal \(B(-\infty)\) for the queer Lie superalgebra ⋮ Rigged configuration descriptions of the crystals B(∞) and B(λ) for special linear Lie algebras ⋮ Crystal \(B(\lambda)\) as a subset of crystal \(B(\infty)\) expressed as tableaux for \(A_n\) type ⋮ Uniform description of the rigged configuration bijection ⋮ A combinatorial description of the Gindikin-Karpelevich formula in type \(A\) ⋮ Descriptions of crystal \(\mathsf{B}(\lambda)\) for \(E_6\) and \(E_7\) types via tableaux and Kashiwara embedding ⋮ On category \(\mathcal O\) over triangular generalized Weyl algebras. ⋮ Path realization of crystal \(B(\infty )\) ⋮ Young tableaux and crystal \(\mathcal B(\infty )\) for the exceptional Lie algebra types ⋮ The flush statistic on semistandard Young tableaux ⋮ Irreducible modules over Khovanov-Lauda-Rouquier algebras of type \(A_n\) and semistandard tableaux ⋮ Generalized Young walls for classical Lie algebras ⋮ Integration on $p$-adic groups and crystal bases ⋮ Using rigged configurations to model \(B(\infty)\) ⋮ Rigged configurations for all symmetrizable types ⋮ Young tableaux and crystal \(\mathcal B(\infty)\) for finite simple Lie algebras ⋮ Alcove path model for \(B(\infty)\) ⋮ Nakajima Monomials and Crystals for Special Linear Lie Algebras ⋮ Lusztig data of Kashiwara-Nakashima tableaux in type D ⋮ Unnamed Item ⋮ Atomic decomposition of characters and crystals ⋮ The crystal ℬ(∞) and extended Nakajima monomials ⋮ Candidate for the crystal \(B_{(-\infty)}\) for the queer Lie superalgebra ⋮ PBW Bases and Marginally Large Tableaux in Types B and C ⋮ Crystal ℬ(∞) for Quantum Affine Algebras: A Young Wall Description

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