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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
##### Keywords:
quantum groups; crystal graph; generalized Young tableaux
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