Categorification of tensor powers of the vector representation of $U_q(\mathfrak{gl}(1|1))$

Abstract

We consider the monoidal subcategory of finite dimensional representations of $U_q(\mathfrak{gl}(1|1))$ generated by the vector representation, and we provide a diagram calculus for the intertwining operators, which allows to compute explicitly the canonical basis. We construct then a categorification of these representations and of the action of both $U_q(\mathfrak{gl}(1|1))$ and the intertwining operators using subquotient categories of the BGG category $\mathcal{O}({\mathfrak{gl}}_n)$.

This is a revised version, with many corrections and improvements. This article is part of the author's PhD thesis

References in corpus (3)

• 2-Kac-Moody algebras
• Knot invariants and higher representation theory
• The Alexander polynomial as quantum invariant of links

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• Strands algebras and the affine highest weight property for equivariant hypertoric categories