Categorification and Higher Representation Theory
About this Title
Anna Beliakova, Universität Zürich, Zürich, Switzerland and Aaron D. Lauda, University of Southern California, Los Angeles, CA, Editors
Publication: Contemporary Mathematics
Publication Year: 2017; Volume 683
ISBNs: 978-1-4704-2460-2 (print); 978-1-4704-3689-6 (online)
The emergent mathematical philosophy of categorification is reshaping our view of modern mathematics by uncovering a hidden layer of structure in mathematics, revealing richer and more robust structures capable of describing more complex phenomena. Categorified representation theory, or higher representation theory, aims to understand a new level of structure present in representation theory. Rather than studying actions of algebras on vector spaces where algebra elements act by linear endomorphisms of the vector space, higher representation theory describes the structure present when algebras act on categories, with algebra elements acting by functors. The new level of structure in higher representation theory arises by studying the natural transformations between functors. This enhanced perspective brings into play a powerful new set of tools that deepens our understanding of traditional representation theory.
This volume exhibits some of the current trends in higher representation theory and the diverse techniques that are being employed in this field with the aim of showcasing the many applications of higher representation theory.
The companion volume (Contemporary Mathematics, Volume 684) is devoted to categorification in geometry, topology, and physics.
Graduate students and research mathematicians interested in representation theory, category theory, and geometry.
Table of Contents
- Ivan Losev – Rational Cherednik algebras and categorification
- Olivier Dudas, Michela Varagnolo and Eric Vasserot – Categorical actions on unipotent representations of finite classical groups
- Jonathan Brundan and Nicholas Davidson – Categorical actions and crystals
- Anthony M. Licata – On the 2-linearity of the free group
- Michael Ehrig, Catharina Stroppel and Daniel Tubbenhauer – The Blanchet-Khovanov algebras
- G. Lusztig – Generic character sheaves on groups over $\mathbf k[\epsilon ]/(\epsilon ^r)$
- Diego Berdeja Suárez – Integral presentations of quantum lattice Heisenberg algebras
- You Qi and Joshua Sussan – Categorification at prime roots of unity and hopfological finiteness
- Ben Elias – Folding with Soergel bimodules
- Lars Thorge Jensen and Geordie Williamson – The p-canonical basis for Hecke algebras