Crystal bases of modified quantized enveloping algebras and a double RSK correspondence

Details Crystal bases of modified quantized enveloping algebras and a double RSK correspondence Crystal bases of modified quantized enveloping algebras and a double RSK correspondence

2010-02-08

arxiv.org/abs/1002.1509v2

Mathematics

Representation Theory

30 pages

Scientific paper

The crystal base of the modified quantized enveloping algebras of type $A_{+\infty}$ or $A_\infty$ is realized as a set of integral bimatrices. It is obtained by describing the decomposition of the tensor product of a highest weight crystal and a lowest weight crystal into extremal weight crystals, and taking its limit using a tableaux model of extremal weight crystals. This realization induces in a purely combinatorial way a bicrystal structure of the crystal base of the modified quantized enveloping algebras and hence its Peter-Weyl type decomposition generalizing the classical RSK correspondence.

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