Littelmann, Peter Crystal graphs and Young tableaux. (English) Zbl 0831.17004 J. Algebra 175, No. 1, 65-87 (1995). 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 \(A\), \(B\), \(C\), \(D\), \(E_6\), \(G_2\). Reviewer: Stefano Capparelli (Roma) Cited in 2 ReviewsCited in 48 Documents MSC: 17B37 Quantum groups (quantized enveloping algebras) and related deformations 05E10 Combinatorial aspects of representation theory 05E05 Symmetric functions and generalizations Keywords:quantum groups; crystal graph; generalized Young tableaux PDFBibTeX XMLCite \textit{P. Littelmann}, J. Algebra 175, No. 1, 65--87 (1995; Zbl 0831.17004) Full Text: DOI