Geodesic
Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal
Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020).

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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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     author = {Kvinge, Henry and Vazirani, Monica},
     title = {Categorifying the tensor product of the {Kirillov-Reshetikhin} crystal {B1,1} and a fundamental crystal},
     journal = {Discrete mathematics & theoretical computer science},
     publisher = {mathdoc},
     volume = {DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016)},
     year = {2020},
     doi = {10.46298/dmtcs.6388},
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     url = {http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6388/}
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Kvinge, Henry; Vazirani, Monica. Categorifying the tensor product of the Kirillov-Reshetikhin crystal B1,1 and a fundamental crystal. Discrete mathematics & theoretical computer science, DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016), DMTCS Proceedings, 28th International Conference on Formal Power Series and Algebraic Combinatorics (FPSAC 2016) (2020). doi : 10.46298/dmtcs.6388. http://geodesic.mathdoc.fr/articles/10.46298/dmtcs.6388/

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