Categorified Jones-Wenzl projectors: a comparison
type: Item
instance of: scholarly article
zbMATH Open document ID: 1329.17014
author: Catharina Stroppel
author: Joshua Sussan
publication date: 2014-08-12T00:00:00Z
full work available at URL: https://arxiv.org/abs/1105.3038
Mathematics Subject Classification ID: 17B37
Mathematics Subject Classification ID: 57M27
Mathematics Subject Classification ID: 20C08
zbMATH DE Number: 6329447
zbMATH Keywords: Jones-Wenzl projector
zbMATH Keywords: categorification
zbMATH Keywords: Jones polynomial
MaRDI profile type: Publication
arXiv ID: 1105.3038
arXiv classification: math.RT
arXiv classification: math.GT
title: Categorified Jones-Wenzl projectors: a comparison
review text: The Jones-Wenzl projector is an idempotent endomorphism of a tensor power of the natural representation of the quantum group \(U_q(\mathfrak{sl}_2)\). It plays an important role in the definition and construction of Reshetikhin-Turaev invariants of \(3\)-manifolds.NEWLINENEWLINEIn this paper the authors compare the Lie theoretic and topological categorifications of the Jones-Wenzl projector and explicitly describe the relationship between the two. They also show how the Lie theoretic categorification of the Jones-Wenzl projector can be used to categorify the colored Jones polynomial using a certain cabling procedure starting from a categorification of the ordinary Jones polynomial.NEWLINENEWLINEFor the entire collection see [Zbl 1285.00037].
reviewed by: Volodymyr Mazorchuk
description: scientific article; zbMATH DE number 6329447