The application of tau-tilting theory to Hecke algebras

点击翻译按钮获取中文摘要

In this academic year, I have written down three papers with my collaborators, the first one is jointed with Kengo Miyamoto on the τ-tilting finiteness of tensor products between simply connected algebras, the second one is jointed with Toshitaka Aoki on the τ-tilting finiteness of blocks of Schur algebras, the last one is jointed with Yingying Zhang on the number of support τ-tilting modules over trivial extensions of gentle tree algebras.Through my own work and the collaboration with Aoki, I have got a complete result for the τ-tilting finiteness of Schur algebras. Since there is a deep connection between Schur algebras and Hecke algebras of type A, we have actually got some progress on this project.