Higher Representation Theory

Abstract

Representation theory is a field of mathematics with applications across the breadth of mathematical study in fields as diverse as number theory and physics. The study of higher (or categorical) representation theory is a modern set of tools that provides new insights into representation theoretic phenomena. This project aims to study categorified quantum groups and, in particular, the categorifications provided by diagrammatic algebras. The project aims to further develop the theory of Khovanov-Lauda-Rouquier (KLR) algebras, providing important foundational results for future research to build upon.

Related publications (3)

Singularities of schubert varieties within a right cell

M Lanini, PJ McNamara

2021-01-01

We describe an algorithm which pattern embeds, in the sense of Woo–Yong, any Bruhat interval of a symmetric group into an interval..

Folding KLR algebras

PJ McNamara

2019-10-01

This paper develops the theory of KLR algebras with a Dynkin diagram automorphism. This is foundational material intended to allow..

Face functors for KLR algebras

PJ Mcnamara, P Tingley

2017-01-01

Simple representations of KLR algebras can be used to realize the infinity crystal for the corresponding symmetrizable Kac-Moody a..