相关论文: Categorification of the Jones-Wenzl Projectors
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 study the representation theory of the smallest quantum group and its categorification. The first part of the paper contains an easy visualization of the 3j-symbols in terms of weighted signed line arrangements in a fixed triangle and…
Let p an integer. We define a family of idempotents (and nilpotents) in the Temperley - Lieb algebras at 4p-th roots of unity which generalize the usual Jones-Wenzl idempotents. These new idempotents correspond to finite dimentional simple…
We describe algebraically, diagrammatically and in terms of weight vectors, the restriction of tensor powers of the standard representation of quantum $\mathfrak{sl}_2$ to a coideal subalgebra. We realise the category as module category…
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 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…
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…
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 introduce a quotient of the affine Temperley-Lieb category that encodes all weight-preserving linear maps between finite-dimensional sl(2)-representations. We study the diagrammatic idempotents that correspond to projections onto…
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.…
Given any diagram of a link, we define on the cube of Kauffman's states a "2-complex" whose homology is an invariant of the associated framed links, and such that the graded Euler characteristic reproduces the unnormalized Kauffman bracket.…
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 construct and study a lift of Jones-Wenzl projectors to the setting of Khovanov spectra, and provide a realization of such lifted projectors via a Cooper-Krushkal-like sequence of maps. We also give a polynomial action on the 3-strand…
We construct a bigraded cohomology theory of links whose Euler characteristic is the Jones polynomial.
Trivalent plane graphs are used in various areas of mathematics which relate for instance to the colored Jones polynomial, invariants of 3-manifolds and quantum computation. Their evaluation is based on computations in the Temperley-Lieb…
We construct a categorification of the maximal commutative subalgebra of the type $A$ Hecke algebra. Specifically, we propose a monoidal functor from the (symmetric) monoidal category of coherent sheaves on the flag Hilbert scheme to the…
A sequence of Temperley-Lieb algebra elements corresponding to torus braids with growing twisting numbers converges to the Jones-Wenzl projector. We show that a sequence of categorification complexes of these braids also has a limit which…
The Temperley-Lieb algebra is a fundamental component of SU(2) topological quantum field theories. We construct chain complexes corresponding to minimal idempotents in the Temperley-Lieb algebra. Our results apply to the framework which…
This preprint comprises the first four out of five chapters of the Master's thesis I wrote 2022 under the supervision of Catharina Stroppel and Paul Wedrich at the University of Bonn titled "Categorified Jones-Wenzl projectors and…
We construct special idempotents in $\mathrm{End}_{U_q(\mathfrak{sl}_2)}(M(\mu)\otimes V_1^{\otimes n})$ like the Jones Wenzl projector where $M(\mu)$ is Verma module whose highest weight is $\mu$ and $V_1$ is $2$-dimensional irreducible…