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A generators and relations description of a representation category of Uq(gl(1|1))

Grant, Jonathan

A generators and relations description of a representation category of Uq(gl(1|1)) Thumbnail


Authors

Jonathan Grant



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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