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Crystal graphs and Young tableaux. (English) Zbl 0831.17004
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 \(A\), \(B\), \(C\), \(D\), \(E_6\), \(G_2\).

MSC:
17B37 Quantum groups (quantized enveloping algebras) and related deformations
05E10 Combinatorial aspects of representation theory
05E05 Symmetric functions and generalizations
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