CMI PhD Research Seminar
Date: Monday, 21 October 2024
Time: 02:00 - 03:00 PM
Venue: Seminar Hall
A q-analogue of the combinatorial category FI
Sadhanandh Vishwanath B
Chennai Mathematical Institute.
21-10-24

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Abstract

The representation theory of the category FI, which consists of finite sets and injections,(along with its variants), has gained significant interest in the past decade. The study of these combinatorial categories and their modules has offered tools for proving various results related to representation stability and polynomial growth in S_n (or its variants) representations. This involves studying a compatible family representations of all symmetric group as a single object.

Similarly, we aimed to develop a q-analogue (the q-FI category) in which the symmetric groups are replaced by the Iwahori-Hecke algebras of Type A. Although there have been a few very recent studies on such categories at specific values, there is no generic category and its representation theory available. I this talk, I will explain our approach in developing a generic framework, inspired by Solomon's work on q-rook monoids, which uses the Bruhat decomposition for GL_n and its associated reductive monoid M_n.