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Categorification of Verma Modules, tensor products and the Temperley-Lieb algebra Vaz, Pedro

Description

In this talk I will review the program of categorification of Verma modules of symmetrizable quantum Kac-Moody algebras and extend it to a categorification of tensor products of a Verma module and several integrable irreducibles. In the last part of the talk I will consider the case of $\mathfrak{sl}(2)$ and explain how its categorifications are endowed with an action of the Temperley-Lieb algebra of type B with two parameters. The material presented is based upon several collaborations with Grégoire Naisse, Ruslan Maksimau and Abel Lacabanne.

Item Metadata

Title
Categorification of Verma Modules, tensor products and the Temperley-Lieb algebra
Creator
Vaz, Pedro
Publisher
Banff International Research Station for Mathematical Innovation and Discovery
Date Issued
2019-12-02T11:11
Description
In this talk I will review the program of categorification of Verma modules of symmetrizable quantum Kac-Moody algebras and extend it to a categorification of tensor products of a Verma module and several integrable irreducibles. In the last part of the talk I will consider the case of $\mathfrak{sl}(2)$ and explain how its categorifications are endowed with an action of the Temperley-Lieb algebra of type B with two parameters. The material presented is based upon several collaborations with Grégoire Naisse, Ruslan Maksimau and Abel Lacabanne.
Extent
67.0 minutes
Subject
Mathematics; Nonassociative rings and algebras; Category theory; homological algebra; Representation theory
Type
Moving Image
File Format
video/mp4
Language
eng
Notes
Author affiliation: Université catholique de Louvain
Series
BIRS Workshop Lecture Videos (Oaxaca de Juárez (Mexico))
Date Available
2020-05-31
Provider
Vancouver : University of British Columbia Library
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International
DOI
10.14288/1.0391067
URI
http://hdl.handle.net/2429/74611
Affiliation
Non UBC
Peer Review Status
Unreviewed
Scholarly Level
Faculty
Rights URI
http://creativecommons.org/licenses/by-nc-nd/4.0/
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Attribution-NonCommercial-NoDerivatives 4.0 International