OIST Representation Theory Seminar

Speaker: Qi Wang, Osaka University

Title: On \(τ\)-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.

Zoom info can be found on the seminar webpage.