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

Grant, Jonathan¹

¹Department of Mathematical Sciences, Durham University, Science Laboratories, South Rd., Durham DH1 3LE, UK

Algebraic and Geometric Topology, Tome 16 (2016) no. 1, pp. 509-539

Résumé

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.

Détail

DOI : 10.2140/agt.2016.16.509

Classification : 17B37, 57M25
Keywords: skew Howe duality, diagram calculus, knot polynomial, quantum group

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