Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal - Archive ouverte HAL Access content directly
Conference Papers Discrete Mathematics and Theoretical Computer Science Year : 2020

Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal

Abstract

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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Dates and versions

hal-02168130 , version 1 (28-06-2019)

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Henry Kvinge, Monica Vazirani. Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨10.46298/dmtcs.6388⟩. ⟨hal-02168130⟩
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