Data
- 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
Abstract
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:
A very similar approach works for the corresponding categories of -modules as well
as we show in an extra section.
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