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

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 $\mathrm{Irr}({\mathcal{O}}_n)$ defined by Bernstein-Frenkel-Khovanov. Further properties of the $\mathfrak{q}(2)$-crystal $\mathrm{Irr}({\mathcal{O}}_n)$ are also discussed.

20 pages, minor changes are made in v.2, Remark 2.3 is inserted with minor corrections in v.3, to appear in Algebras and Representation Theory

References in corpus (2)

• 2-Kac-Moody algebras
• Super duality and Crystal bases for quantum orthosymplectic superalgebras