- Title: Super -Howe duality and web categories
- Authors: Daniel Tubbenhauer, Pedro Vaz and Paul Wedrich
- Status: Algebr. Geom. Topol. 17-6 (2017), 3703-3749. Last update: Tue, 21 Nov 2017 19:09:56 GMT
- ArXiv link: http://arxiv.org/abs/1504.05069
- ArXiv version = 0.99 published version
- LaTex Beamer presentation: Slides1, Slides2, Slides3, Slides4, Slides5, Slides6
- Poster: Poster
We use super -Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of -modules (and more generally -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.
A few extra words
We discuss a machine that “takes dualities
and produces diagrammatic presentations of the related
representation theoretical categories”.
Specifically, we feed the machine
with super -Howe duality
between the superalgebra and .
We construct diagrammatic presentations of an idempotented form of the Iwahori-Hecke algebra as well as of categories of -modules by using the “green-red” web categories and . Morphisms in these -linear categories are combinations of planar, upwards oriented, trivalent graphs with edges labeled by positive integers and colored black, green or red modulo local relations.
An example of a green-red web is: