Shiquan Ruan from Beijing

Abstract: |
Let $\text{coh-}X$ be the category of coherent sheaves over a weighted projective line $X$ and let $D^b(\text{coh-}X)$ be its bounded derived category. In this talk we will focus on the study of the right and left mutation functors arising in $D^b(\text{coh-}X)$ attached to certain line bundles. We first show that these mutation functors give rise to simple reflections for the Weyl group of the star shaped quiver $Q$ associated with $X$. By further dealing with the Ringel-Hall algebra of $X$, we show that these functors provide a realization for Tits’ automorphisms of the Kac-Moody algebra $g_Q$ of $Q$, as well as for Lusztig’s symmetries of the quantum enveloping algebra of $g_Q$. |