Volume 17, issue 6 (2017)

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Super $q$–Howe duality and web categories

Daniel Tubbenhauer, Pedro Vaz and Paul Wedrich

Algebraic & Geometric Topology 17 (2017) 3703–3749
Abstract

We use super $q$–Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of ${\mathfrak{g}\mathfrak{l}}_{N}$–modules (and, more generally, ${\mathfrak{g}\mathfrak{l}}_{N|M}$–modules) whose objects are tensor generated by exterior and symmetric powers of the vector representations. As an application, we give a representation-theoretic explanation and a diagrammatic version of a known symmetry of colored HOMFLYPT polynomials.

Keywords
web categories, quantum Howe duality, quantum Lie superalgebras, colored HOMFLY-PT polynomials
Mathematical Subject Classification 2010
Primary: 57M25, 81R50