Tuesday, July 13, 2021
Tiago Cruz, Quality of split quasi-hereditary covers and Ringel duality.
In this talk, we will explore some split quasi-hereditary covers and their
quality. For example, the block algebras of the classical category
𝒪, together with their projective-injective module, are split
quasi-hereditary covers of subalgebras of coinvariant algebras.
We will talk about a new generalization of relative dominant (and
codominant) dimension with respect to a summand of a characteristic tilting
module and how this is a tool to the study of split quasi-hereditary covers.
Using these concepts we reprove Soergel's theorem that block algebras of the
BGG category 𝒪 are Ringel self-dual.