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arXiv · 1407.6457

A categorification of $\mathfrak{q}(2)$-crystals

Dimitar Grantcharov·Ji Hye Jung·Seok-Jin Kang·Myungho Kim
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Abstract

We provide a categorification of $\mathfrak{q}(2)$-crystals on the singular $\mathfrak{gl}_{n}$-category ${\mathcal O}_{n}$. Our result extends the $\mathfrak{gl}_{2}$-crystal structure on ${\rm Irr} ({\mathcal O}_{n})$ defined by Bernstein-Frenkel-Khovanov. Further properties of the ${\mathfrak q}(2)$-crystal ${\rm Irr}({\mathcal O}_{n})$ are also discussed.

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Dimitar Grantcharov, Ji Hye Jung, Seok-Jin Kang, Myungho Kim. 2014-07-24. A categorification of $\mathfrak{q}(2)$-crystals. https://arxiv.org/abs/1407.6457

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