A generators and relations description of a representation category of U-q (gl(1 vertical bar 1))

作者：Grant Jonathan^*

来源：Algebraic and Geometric Topology, 2016, 16(1): 509-539.

DOI：10.2140/agt.2016.16.509

We use the technique of quantum skew Howe duality to investigate the monoidal category generated by exterior powers of the standard representation of U-q(gl(1 vertical bar 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. TLhe technique also gives a useful connection between a system of symmetries on circle plus(m) (U) over dot(q)(gl(m)) and the braiding on the category of U-q(gl(1 vertical bar 1))-representations which can be used to construct the Alexander polynomial and coloured variants.

• 出版日期2016