Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal
Henry Kvinge  1  , Monica Vazirani  1  
1 : Department of Mathematics [Davis]  -  Website
University of California, One Shields Av., Davis, CA 95616 -  États-Unis

We use Khovanov-Lauda-Rouquier (KLR) algebras to categorify a crystal isomorphism between a funda- mental crystal and the tensor product of a Kirillov-Reshetikhin crystal and another fundamental crystal, all in affine type. The nodes of the Kirillov-Reshetikhin crystal correspond to a family of “trivial” modules. The nodes of the fun- damental crystal correspond to simple modules of the corresponding cyclotomic KLR algebra. The crystal operators correspond to socle of restriction and behave compatibly with the rule for tensor product of crystal graphs. 

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