On $\tau$-tilting finiteness of Schur algebras

Abstract: Support $\tau$-tilting modules are introduced by Adachi, Iyama and Reiten in 2012 as a generalization of classical tilting modules. One of the importance of these modules is that they are bijectively corresponding to many other objects, such as two-term silting complexes and left finite semibricks. Let $V$ be an $n$-dimensional vector space over an algebraically closed field $\mathbb{F}$ of characteristic $p$. Then, the Schur algebra $S(n,r)$ is defined as the endomorphism ring $\mathsf{End}_{\mathbb{F}G_r}\left ( V^{\otimes r} \right )$ over the group algebra $\mathbb{F}G_r$ of the symmetric group $G_r$. In this talk, we discuss when the Schur algebra $S(n,r)$ has only finitely many pairwise non-isomorphic basic support $\tau$-tilting modules.

combinatoricsquantum algebrarings and algebrasrepresentation theory

Audience: researchers in the topic

OIST representation theory seminar

Series comments: Timings of this seminar may vary from week to week.