Representation stability for diagram algebras
Peter Patzt
TL;DR
This paper introduces stability categories for diagram algebras to analyze their representation stability, focusing on Temperley--Lieb, Brauer, and partition algebras, extending previous categorical frameworks.
Contribution
It develops new stability categories for diagram algebras, enabling the study of their representation stability properties in a unified framework.
Findings
Established stability properties for Temperley--Lieb algebras
Proved representation stability for Brauer algebras
Analyzed partition algebras within the stability category framework
Abstract
We introduce stability categories for diagram algebras---analogues to Randal-Williams and Wahl's homogeneous categories. We use these to study representation stability properties of the Temperley--Lieb algebras, the Brauer algebras, and the partition algebras.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra