Work

Diagrammatics for the smallest quantum coideal and Jones–Wenzl projectors

Year: 2025

Type: article

Abstract: 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 realize the category as a module category over the monoidal category of type $\pm 1$ representations in terms of string diagrams and via generators and relations. The idempotents projecting onto the quantized eigenspaces are described as type $B/D$ analogues of Jones–Wenzl projectors. As an application, we introduce and give recursive formulas for analogues of $\Theta$ -networks.

Source: Glasgow Mathematical Journal

DOI: 10.1017/s0017089524000387

Authors: Catharina Stroppel, Zbigniew Wojciechowski

Institutions: University of Bonn, Technische Universität Dresden

Language: English

Topic: Algebraic structures and combinatorial models

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: Hausdorff Center for Mathematics

Award: G5310617150