Symmetric webs, Jones-Wenzl recursions and q-Howe duality

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    David Rose, University of Southern California, United StatesDaniel Tubbenhauer, Denmark
We define and study the category of symmetric sl2-webs. This category is
a combinatorial description of the category of all finite dimensional quantum
sl2-modules. Explicitly, we show that (the additive closure of) the symmetric sl2-spider is (braided monoidally) equivalent to the latter.
Our main tool is a quantum version of symmetric Howe duality.
As a corollary of our construction, we provide new insight into Jones-Wenzl projectors and the colored Jones polynomials.
Original languageEnglish
PublisherarXiv.org
StatePublished - 2015

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