Abstract
We define the notion of representation stability for sequences of modules over the Temperley–Lieb algebras, the Brauer algebras, and the partition algebras in the semisimple setting analogous to Church and Farb. We also find a condition when such sequences are representation stable analogous to Church, Ellenberg, and Farb. To this end, we introduce stability categories for these diagram algebras—analogs to Randal-Williams and Wahl's homogeneous categories. We prove that finitely presented modules over these stability categories give rise to representation stable sequences as long as the parameters ensure semisimplicity.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
