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

@article{Rose2015SymmetricWJ,
  title={Symmetric webs, Jones-Wenzl recursions and \$q\$-Howe duality},
  author={David E. V. Rose and D. Tubbenhauer},
  journal={arXiv: Quantum Algebra},
  year={2015}
}
We define and study the category of symmetric $\mathfrak{sl}_2$-webs. This category is a combinatorial description of the category of all finite dimensional quantum $\mathfrak{sl}_2$-modules. Explicitly, we show that (the additive closure of) the symmetric $\mathfrak{sl}_2$-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… Expand
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