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A Categorification of $\displaystyle {\mathfrak q} (2)$-Crystals |
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| Authors: | Dimitar?Grantcharov |
| Institution: | 1.Department of Mathematics,University of Texas at Arlington,Arlington,USA;2.Department of Mathematical Sciences,Seoul National University,Seoul,Korea;3.Department of Mathematical Sciences and Research Institute of Mathematics,Seoul National University,Seoul,Korea;4.Department of Mathematics,Kyung Hee University,Seoul,Korea |
| 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 \(\text {Irr} ({\mathcal O}_{n})\) induced from the work of Bernstein-Frenkel-Khovanov. Further properties of the \({\mathfrak q}(2)\)-crystal \(\text {Irr} ({\mathcal O}_{n})\) are also discussed. |
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