Jonathan Grant
A generators and relations description of a representation category of Uq(gl(1|1))
Grant, Jonathan
Authors
Abstract
We use the technique of quantum skew Howe duality to investigate the monoidal category generated by exterior powers of the standard representation of Uq(gl(1|1))Uq(gl(1|1)). This produces a complete diagrammatic description of the category in terms of trivalent graphs, with the usual MOY relations plus one additional family of relations. The technique also gives a useful connection between a system of symmetries on ⊕mU̇ q(gl(m))⊕mU̇q(gl(m)) and the braiding on the category of Uq(gl(1|1))Uq(gl(1|1))–representations which can be used to construct the Alexander polynomial and coloured variants.
Citation
Grant, J. (2016). A generators and relations description of a representation category of Uq(gl(1|1)). Algebraic & geometric topology, 16(1), 509-539. https://doi.org/10.2140/agt.2016.16.509
Journal Article Type | Article |
---|---|
Acceptance Date | Jul 6, 2015 |
Online Publication Date | Feb 23, 2016 |
Publication Date | Feb 23, 2016 |
Deposit Date | Mar 8, 2016 |
Publicly Available Date | May 6, 2016 |
Journal | Algebraic and Geometric Topology |
Print ISSN | 1472-2747 |
Electronic ISSN | 1472-2739 |
Publisher | Mathematical Sciences Publishers (MSP) |
Peer Reviewed | Peer Reviewed |
Volume | 16 |
Issue | 1 |
Pages | 509-539 |
DOI | https://doi.org/10.2140/agt.2016.16.509 |
Public URL | https://durham-repository.worktribe.com/output/1417649 |
Related Public URLs | http://arxiv.org/abs/1406.5399 |
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Copyright Statement
First published in Geometry & Topology in 16/1, 2016 published by Mathematical Sciences Publishers. © 2016 Mathematical Sciences Publishers. All rights reserved.
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