Work

Extremal weight projectors

Year: 2017

Type: preprint

Abstract: 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 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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1701.02316

Authors: Queffelec, Hoel, Wedrich, Paul

Institutions: Centre National de la Recherche Scientifique, Université de Montpellier, Institut Montpelliérain Alexander Grothendieck, Imperial College London, Australian National University

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

OpenAlex ID: W2952609081

Cites: 17

Cited by:

Related to: 20