%0 Journal Article
%T A generators and relations description of a representation category of $U_q(\mathfrak{gl}(1|1))$
%A Jonathan Grant
%J Mathematics
%D 2014
%I arXiv
%X We use the technique of quantum skew Howe duality to investigate the monoidal category of exterior powers of the standard representation of $U_q(\mathfrak{gl}(1|1))$. 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 $\bigoplus_m \dot{U}_q(\mathfrak{gl}(m))$ and the braiding on the category of $U_q(\mathfrak{gl}(1|1))$-representations which can be used to construct the Alexander polynomial and coloured variants.
%U http://arxiv.org/abs/1406.5399v1