We categorify the crystal of the modified quantized enveloping algebra associated to a symmetrizable Kac–Moody algebra. Generalizing the result of Chuang–Rouquier, we construct a crystal from an action of the Kac–Moody 2-category on abelian categories. We show that the self-dual indecomposable objects of the categorified quantum group form a crystal, and that it coincides with the crystal B(Ũ_q(g)). A key step is to identify the crystal from Webster's generalized tensor product categorification with the tensor product crystals. As an application, we obtain a categorification of the extremal weight module, the generalization of integrable highest weight modules to arbitrary weights.

발표시간: 10:00 ~ 11:00