Super $q$-Howe duality and web categories

Abstract

We use super $q$-Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of ${\mathfrak{gl}}_N$-modules (and, more generally, ${\mathfrak{gl}}_{N|M}$-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 HOMFLY--PT polynomials.

38 pages, many colored figures, extra section containing new results, added suggestions of two referees, comments welcome

References in corpus (3)

• Symmetric webs, Jones-Wenzl recursions and $q$-Howe duality
• Quadruply-graded colored homology of knots
• A generators and relations description of a representation category of $U_q(\mathfrak{gl}(1|1))$

Cited by in corpus (23)

• Annular Evaluation and Link Homology
• Rational links and DT invariants of quivers
• Invariants of 4-manifolds from Khovanov-Rozansky link homology
• Tangle addition and the knots-quivers correspondence
• Quivers for SL(2) tilting modules
• Generic ${\mathfrak{gl}}_2$-foams, web and arc algebras
• q-holonomic formulas for colored HOMFLY polynomials of 2-bridge links
• DG structures on odd categorified quantum sl(2)
• Ozsvath-Szabo bordered algebras and subquotients of category O
• A note on the gl(m|n) link invariants and the HOMFLY-PT polynomial
• Extremal weight projectors II
• Sandwich cellularity and a version of cell theory
• Quiver Schur algebras and cohomological Hall algebras
• Braid group actions from categorical symmetric Howe duality on deformed Webster algebras
• Transitioning between tableaux and spider bases for Specht modules
• On webs in quantum type $C$
• Trivalent vertices and bordered knot Floer homology in the standard basis
• On a symplectic quantum Howe duality
• Handlebody diagram algebras
• gl(2) foams and the Khovanov homotopy type
• A simple proof of the strong integrality for full colored HOMFLYPT invariants
• Webs of Type P
• A categorification of the skew Howe action on a representation category of $U_q(\mathfrak{gl}(m|n))$