| • | Wednesday, Jun 26, 2019, 9:00 - 10:00, New Main Building 1223 | |
| Prof. Xiuping Su (University of Bath, UK) Towards categorification of quantum Grassmannian cluster algebras | ||
Abstract:Based on a cluster category CM($A$), we construct compatible pairs of matrices $(B(T), L(T))$ from a cluster tilting object $T$ in CM($A$). We show that 1) when the matrix $L$ is constructed from certain special cluster tilting objects, $L$ computes quasi-commutation rules for quasi-commuting quantum minors. 2) Mutation of $(B(T), L(T))$ is consistent with mutation of cluster tilting objects. The goal of this talk is to explain how 1) and 2) lead to a quantum cluster algebra structure on a quantum Grassmannian and thus a categorification of the quantum Grassmannian cluster algebra. | ||