Diagrammatics for dicyclic groups

TL;DR

This paper extends Temperley-Lieb diagrammatics to provide a visual and algebraic framework for understanding the complex representation theory of dicyclic groups, which are subgroups of SU(2).

Contribution

It introduces a novel diagrammatic approach specifically tailored for the complex representation theory of dicyclic groups, expanding the applicability of Temperley-Lieb diagrams.

Findings

Diagrammatic presentation of dicyclic group representations

Extension of Temperley-Lieb diagrams to new algebraic structures

Enhanced understanding of the representation theory of type D subgroups

Abstract

Using that the dicyclic group is the type D subgroup of SU(2), we extend the Temperley-Lieb diagrammatics to give a diagrammatic presentation of the complex representation theory of the dicyclic group.