Crystal graphs and Young tableaux
type: Item
instance of: scholarly article
title: Crystal graphs and Young tableaux
zbMATH Open document ID: 0831.17004
published in: Journal of Algebra
publication date: 1996-02-20T00:00:00Z
review text: Let \(M\) be an integrable module of the quantized enveloping algebra \(U_q (\Phi)\) associated to an irreducible root system \(\Phi\). Kashiwara proved that \(M\) has a crystal base having the structure of a colored oriented graph, which reflects the structure of \(M\). This paper gives a description of the crystal graph in terms of generalized Young tableaux in the case when \(\Phi\) is of type \(A\), \(B\), \(C\), \(D\), \(E_6\), \(G_2\).
reviewed by: Stefano Capparelli
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 05E10
Mathematics Subject Classification ID: 05E05
zbMATH DE Number: 783911
zbMATH Keywords: quantum groups
zbMATH Keywords: crystal graph
zbMATH Keywords: generalized Young tableaux
author: Peter Littelmann
MaRDI profile type: Publication
full work available at URL: jabr.1995.1175
OpenAlex ID: W2039041861
DOI: 10.1006/JABR.1995.1175
Recommended article: Crystal Graphs and the Combinatorics of Young Tableaux
Recommended article: Crystal bases and Young tableaux
Recommended article: Crystal graphs for shifted tableaux
Recommended article: Geometric and combinatorial realizations of crystal graphs
Recommended article: Crystal graphs, key tabloids, and nonsymmetric Macdonald polynomials
Recommended article: Demazure crystals and extended Young diagrams
Recommended article: Geometric crystals on unipotent groups and generalized Young tableaux
Recommended article: The Burge correspondence and crystal graphs
Recommended article: Weight Multiplicities and Young Tableaux Through Affine Crystals
Recommended article: Crystals, semistandard tableaux and cyclic sieving phenomenon
description: scientific article; zbMATH DE number 783911