Generators, projectors, and the Jones-Wenzl algebra

Understand

We investigate a subalgebra of the Temperley-Lieb algebra called the Jones-Wenzl algebra, which is obtained by action of certain Jones-Wenzl projectors.

• This algebra arises naturally in applications to conformal field theory and statistical physics.
• It is also the commutant (centralizer) algebra of the Hopf algebra $U_q(\mathfrak{sl}_2)$ on its type-one modules - this fact is a generalization of the $q$-Schur-Weyl duality of Jimbo.
• In this article, we find two minimal generating sets for the Jones-Wenzl algebra.