Mathematics Seminar
Date: Wednesday, 9 April 2025
Time: 2:00 PM
Venue: Seminar Hall
q-FI category and its representation theory
Sadhanandh Vishwanath B
Chennai Mathematical Institute.
09-04-25

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Abstract

The representation theory of the FI category, comprising finite sets and injections, has attracted considerable interest for its role in studying representation stability and the polynomial growth of S_n representations. A fundamental result in this theory is the Noetherian property of finitely generated FI-modules.

Motivated by this, we aim to develop a q-analogue, the q-FI category, in which the symmetric groups are replaced by the Iwahori???Hecke algebras of type A. We propose two different constructions for defining the q-FI category, which ultimately give rise to the same category.

In this talk, I will focus on one of these constructions, which draws on perspectives from rewriting theory and involves diagrammatic arguments. I will then apply Sam and Snowden's Gröbner theory for q-FI representations to deduce the Noetherian property in this setting.