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arXiv · 1508.03802

Categorifying the tensor product of a level 1 highest weight and perfect crystal in type A

Monica Vazirani
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Abstract

We use Khovanov-Lauda-Rouquier algebras to categorify a crystal isomorphism between a highest weight crystal and the tensor product of a perfect crystal and another highest weight crystal, all in level 1 type A affine. The nodes of the perfect crystal correspond to a family of trivial modules and the nodes of the highest weight crystal correspond to simple modules, which we may also parameterize by $\ell$-restricted partitions. In the case $\ell$ is a prime, one can reinterpret all the results for the symmetric group in characteristic $\ell$. The crystal operators correspond to socle of restriction and behave compatibly with the rule for tensor product of crystal graphs.

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Monica Vazirani. 2015-08-16. Categorifying the tensor product of a level 1 highest weight and perfect crystal in type A. https://arxiv.org/abs/1508.03802

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