Resolution of singularities in representation theory

Speaker:

Tiago Cruz

Affiliation:

Universität Stuttgart/MPIM

Date:

Thu, 13/04/2023 - 15:00 - 16:00

Location:

MPIM Lecture Hall [2]

Parent event:

MPI-Oberseminar [3]

In algebraic geometry, a resolution of singularities is, roughly speaking, a replacement of a local commutative Noetherian ring of infinite global dimension by a local commutative Noetherian ring of finite global dimension. In representation theory, an analogous problem is asking to resolve algebras of infinite global dimension by algebras of finite global dimension through a so-called Schur functor.

In addition, such resolutions should have nicer properties to help us study the representation theory of algebras of infinite global dimension. This motivates us to study split quasi-hereditary covers (in the sense of Rouquier) as these algebraic analogues of resolutions of singularities and measure their quality using generalisations of dominant dimension.

In such a setup, Schur algebras together with the Schur functor resolve group algebras of symmetric groups.

If time permits, we will discuss the connection between Temperley-Lieb algebras and their resolutions.