**Data**

- Title: Symmetric webs, Jones-Wenzl recursions and -Howe duality
- Authors: David Rose and Daniel Tubbenhauer
- Status: Int. Math. Res. Not. (IMRN), 2016-17 (2016), 5249-5290. Last update: Mon, 5 Jan 2015 16:33:17 GMT
- ArXiv link: http://arxiv.org/abs/1501.00915
- ArXiv version differs from the published version
- LaTex Beamer presentation: Slides1, Slides2, Slides3, Slides4, Slides5, Slides6, Slides7, Slides8
- Poster: Poster

**Abstract**

**A few extra words**

By Karoubi completion, we get the whole category of finite dimensional -modules. Thus, it is a striking question if one can give a diagrammatic description of as well.

We provide a new diagrammatic description of the entire category of finite dimensional quantum -modules.

To this end, we introduced our new description of the representation theory of quantum , the category of symmetric -webs akin to the category of “usual” -webs studied by many people (recall that these “usual” -webs give a diagrammatic presentation of the full subcategory of all finite dimensional -modules whose objects are finite tensor products of the fundamental -representations

Our main tool is the usage of symmetric -Howe duality.

In particular, the Jones-Wenzl projectors are included in our picture, but without any recursive formula. Namely, they are directly given as below.

Another corollary of our construction is a “MOY-calculus” for colored Jones polynomials.