Young tableaux and crystal \(\mathcal B(\infty )\) for the exceptional Lie algebra types

DOI10.1016/j.jcta.2011.09.009zbMath1232.05236OpenAlexW1974337466WikidataQ112881841 ScholiaQ112881841MaRDI QIDQ654895

Jin Hong, Hyeonmi Lee

Publication date: 23 December 2011

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2011.09.009

zbMATH Keywords

quantum groupYoung tableaucrystal baseexceptional type Lie algebra

Mathematics Subject Classification ID

Combinatorial aspects of representation theory (05E10)

Related Items (8)

Connecting marginally large tableaux and rigged configurations via crystals ⋮ Rigged configurations and the \(\ast\)-involution ⋮ Description of \(\mathsf {B}(\infty)\) through Kashiwara embedding for Lie algebra types \(E_6\) and \(E_7\) ⋮ Crystal \(B(\lambda)\) as a subset of crystal \(B(\infty)\) expressed as tableaux for \(A_n\) type ⋮ Descriptions of crystal \(\mathsf{B}(\lambda)\) for \(E_6\) and \(E_7\) types via tableaux and Kashiwara embedding ⋮ Young tableaux and crystal \(\mathcal B(\infty)\) for finite simple Lie algebras ⋮ Alcove path model for \(B(\infty)\) ⋮ Crystal ℬ(∞) for Quantum Affine Algebras: A Young Wall Description

Cites Work

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• Affine structures and a tableau model for \(E_{6}\) crystals
• Young tableaux and crystal \(\mathcal B(\infty)\) for finite simple Lie algebras
• Adjoint crystals and Young walls for \(U_q(\widehat{sl}_2)\)
• On crystal bases of the \(q\)-analogue of universal enveloping algebras
• Crystal bases and Young tableaux
• A Littlewood-Richardson rule for symmetrizable Kac-Moody algebras
• Crystal bases and tensor product decompositions of \(U_ q(G_ 2)\)- modules
• The crystal base and Littelmann's refined Demazure character formula
• Crystal graphs for representations of the \(q\)-analogue of classical Lie algebras
• Geometric construction of crystal bases
• Polyhedral realizations of crystal bases for quantized Kac-Moody algebras
• Crystal graphs and Young tableaux
• Paths and root operators in representation theory
• Extended Nakajima monomials and crystal \({\mathcal B}(\infty)\) for finite simple Lie algebras
• Crystal ℬ(∞) for Quantum Affine Algebras: A Young Wall Description
• Quivers, Perverse Sheaves, and Quantized Enveloping Algebras

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