English

The pop-switch planar algebra and the Jones-Wenzl idempotents

Quantum Algebra 2015-01-21 v1 General Topology Representation Theory

Abstract

The Jones-Wenzl idempotents are elements of the Temperley-Lieb planar algebra that are important, but complicated to write down. We will present a new planar algebra, the pop-switch planar algebra, which contains the Temperley-Lieb planar algebra. It is motivated by Jones' idea of the graph planar algebra of type AnA_n. In the tensor category of idempotents of the pop-switch planar algebra, the nnth Jones-Wenzl idempotent is isomorphic to a direct sum of n+1n+1 diagrams consisting of only vertical strands.

Keywords

Cite

@article{arxiv.1501.04672,
  title  = {The pop-switch planar algebra and the Jones-Wenzl idempotents},
  author = {Ellie Grano and Stephen Bigelow},
  journal= {arXiv preprint arXiv:1501.04672},
  year   = {2015}
}