Related papers: An infinite torus braid yields a categorified Jone…
We show that the limiting Khovanov chain complex of any infinite positive braid categorifies the Jones-Wenzl projector. This result extends Lev Rozansky's categorification of the Jones-Wenzl projectors using the limiting complex of infinite…
The Jones--Wenzl projections are a special class of elements of the Temperley--Lieb algebra. We prove that the coefficient appearing in the Jones--Wenzl projection is given by a generating function of combinatorial objects, called Dyck…
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…
We construct a categorification of the quantum sl_3 projectors, the sl_3 analog of the Jones-Wenzl projectors, as the stable limit of the complexes assigned to k-twist torus braids (as k goes to infinity) in a suitably shifted version of…
The Jones-Wenzl projectors are particular elements of the Temperley-Lieb algebra essential to the construction of quantum 3-manifold invariants. As a first step toward categorifying quantum 3-manifold invariants, Cooper and Krushkal…
We use the machinery of categorified Jones-Wenzl projectors to construct a categorification of a type A Reshetikhin-Turaev invariant of oriented framed tangles where each strand is labeled by an arbitrary finite-dimensional representation.…
We survey some recent results in hopfological algebra and the program of categorification at prime roots of unity. A categorical Jones-Wenzl projector at prime roots of unity is studied, and it is shown that this projector is hopfologically…
We present a method of defining projectors in the virtual Temperley-Lieb algebra, that generalizes the Jones-Wenzl projectors in Temperley-Lieb algebra. We show that the projectors have similar properties with the Jones-Wenzl projectors,…
A relation for the Jones-Wenzl projector is proven. It has the following consequence for representations of the Temperley-Lieb algebra on tensor product spaces: if such a representation is built from a Hermitian $n \times n$ matrix $T$ of…
For a prime number $p$ and any natural number $n$ we introduce, by giving an explicit recursive formula, the $p$-Jones-Wenzl projector ${}^p\operatorname{JW}_n$, an element of the Temperley-Lieb algebra $TL_n(2)$ with coefficients in…
We give a diagrammatic presentation for the category of Soergel bimodules for the dihedral group W . The (two-colored) Temperley-Lieb category is embedded inside this category as the degree 0 morphisms between color-alternating objects. The…
We explicitly describe a relationship between the Lie theoretic and topological categorification of the Jones-Wenzl projector The two categorifications appear in arXiv:1007.4680 and arXiv:1005.5117 respectively.
We study the relation between a coefficient of an element of the Jones--Wenzl projection in the Temperley--Lieb algebra of type $D$ and an enumeration of Dyck tilings. The coefficient can be non-recursively expressed as an enumerative…
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…
The Jones-Wenzl projectors play a central role in quantum topology, underlying the construction of SU(2) topological quantum field theories and quantum spin networks. We construct chain complexes whose graded Euler characteristic is the…
We show that the limiting unicolored $\mathfrak{sl}(N)$ Khovanov-Rozansky chain complex of any infinite positive braid categorifies a highest-weight projector. This result extends an earlier result of Cautis categorifying highest-weight…
The Jones-Wenzl idempotents of the Temperley-Lieb algebra are celebrated elements defined over characteristic zero and for generic loop parameter. Given pointed field $(R, \delta)$, we extend the existing results of Burrull, Libedinsky and…
The two-colored Temperley-Lieb algebra $2\mathrm{TL}_R({}_s {n})$ is a generalization of the Temperley-Lieb algebra. The analogous two-colored Jones-Wenzl projector $\mathrm{JW}_R({}_s {n}) \in 2\mathrm{TL}_R({}_s {n})$ plays an important…
We define an infinite chain of subcategories of the partition category by introducing the left-height ($l$) of a partition. For the Brauer case, the chain starts with the Temperley-Lieb ($l=-1$) and ends with the Brauer ($l=\infty$)…
We categorify all the Reshetikhin-Turaev tangle invariants of type A. Our main tool is a categorification of the generalized Jones-Wenzl projectors (a.k.a. clasps) as infinite twists. Applying this to certain convolution product varieties…