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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 glN–modules (and, more generally, glN|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.

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Keywords
web categories, quantum Howe duality, quantum Lie superalgebras, colored HOMFLY-PT polynomials
Mathematical Subject Classification 2010
Primary: 57M25, 81R50
References
Publication
Received: 16 October 2016
Revised: 1 March 2017
Accepted: 12 March 2017
Published: 4 October 2017
Authors
Daniel Tubbenhauer
Mathematisches Institut
Universität Bonn
Bonn
Germany
http://www.math.uni-bonn.de/people/dtubben/
Pedro Vaz
Institut de Recherche en Mathématique et Physique
Université Catholique de Louvain
Louvain-la-Neuve
Belgium
http://perso.uclouvain.be/pedro.vaz/
Paul Wedrich
Department of Mathematics
Imperial College London
London
United Kingdom
http://paul.wedrich.at/