Stratifying systems, τ-tilting theory and g-vectors

Abstract: In this talk we will talk about the relationship between the stratifying systems defined by Erdmann and Sáenz and the τ-tilting theory introduced by Adachi Iyama and Reiten. In the first part of the talk we will start the talk explaining how the properties of the mutation process on tau-tilting pairs enables us to build at least one stratifying from every τ-rigid module.

In the second part of the talk we will change gears slightly and speak about Cartan matrices as an invariant for stratifying systems, as it was recently proposed by Marcos, Mendoza and Sáenz. In particular we will speak how the Cartan matrix for a stratifying systems induced by a τ-rigid module can be computed using the g-vectors of the said τ-rigid module.

This is a report on joint work with Octavio Mendoza and Corina Sáenz.

arxiv.org/abs/1904.11903

arxiv.org/abs/2111.11376

combinatoricscategory theoryrepresentation theory

Audience: researchers in the topic

( slides )

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The TRAC Seminar - Théorie de Représentations et ses Applications et Connections

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