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Crystal graph of the modified quantum group of type $A_{+\infty}$ and RSK algorithm
Algebra & Discrete Mathematics| Speaker: | Jae-Hoon Kwon, University of Seoul, Korea |
| Location: | 1147 MSB |
| Start time: | Fri, Nov 19 2010, 2:10PM |
Description
We give a new combinatorial realization of the crystal base
of the modified quantized enveloping algebras of affine type
$A_{+\infty}$ (arXivmathRT/1002.1509). 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
algebra and hence its Peter-Weyl type decomposition generalizing the
classical RSK correspondence.