Extremal weight projectors

Abstract

We introduce a quotient of the affine Temperley–Lieb category that encodes all weight-preserving linear maps between finite-dimensional sl2-representations.We study the diagrammatic idempotents that correspond to projections onto extremal weight spaces and find that they satisfy similar properties as Jones–Wenzl projectors, and that they categorify the Chebyshev polynomials of the first kind. This gives a categorification of the Kauffman bracket skein algebra of the annulus, which is well adapted to the task of categorifying the multiplication on the Kauffman bracket skein module of the torus. Show more