Volume 16, issue 1 (2016)

Download this article
Download this article For screen
For printing
Recent Issues

Volume 24
Issue 6, 2971–3570
Issue 5, 2389–2970
Issue 4, 1809–2387
Issue 3, 1225–1808
Issue 2, 595–1223
Issue 1, 1–594

Volume 23, 9 issues

Volume 22, 8 issues

Volume 21, 7 issues

Volume 20, 7 issues

Volume 19, 7 issues

Volume 18, 7 issues

Volume 17, 6 issues

Volume 16, 6 issues

Volume 15, 6 issues

Volume 14, 6 issues

Volume 13, 6 issues

Volume 12, 4 issues

Volume 11, 5 issues

Volume 10, 4 issues

Volume 9, 4 issues

Volume 8, 4 issues

Volume 7, 4 issues

Volume 6, 5 issues

Volume 5, 4 issues

Volume 4, 2 issues

Volume 3, 2 issues

Volume 2, 2 issues

Volume 1, 2 issues

The Journal
About the Journal
Editorial Board
Subscriptions
 
Submission Guidelines
Submission Page
Policies for Authors
Ethics Statement
 
ISSN 1472-2739 (online)
ISSN 1472-2747 (print)
Author Index
To Appear
 
Other MSP Journals
A generators and relations description of a representation category of $U_q(\mathfrak{gl}(1|1))$

Jonathan Grant

Algebraic & Geometric Topology 16 (2016) 509–539
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)). 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 mU̇q(gl(m)) and the braiding on the category of Uq(gl(1|1))–representations which can be used to construct the Alexander polynomial and coloured variants.

Keywords
skew Howe duality, diagram calculus, knot polynomial, quantum group
Mathematical Subject Classification 2010
Primary: 17B37
Secondary: 57M25
References
Publication
Received: 2 December 2014
Revised: 13 May 2015
Accepted: 6 July 2015
Published: 23 February 2016
Authors
Jonathan Grant
Department of Mathematical Sciences
Durham University
Science Laboratories
South Rd.
Durham DH1 3LE
UK
http://www.maths.dur.ac.uk/users/jonathan.grant/