Work

The Geometry of Generalised Spin${}^r$ Spinors on Projective Spaces

Year: 2025

Type: article

Abstract: In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spin$^r$ context. We find new invariant spin$^r$ spinors on the projective spaces $\mathbb{CP}^n$, $\mathbb{HP}^n$, and the Cayley plane $\mathbb{OP}^2$ for all their homogeneous realisations. Specifically, for each of these realisations, we provide a complete description of the space of invariant spin$^r$ spinors for the minimum value of $r$ for which this space is non-zero. Additionally, we demonstrate some geometric implications of the existence of special spin$^r$ spinors on these spaces.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2025.017

Authors: Diego Artacho, Jordan Hofmann

Language: English

Topic: Algebraic and Geometric Analysis

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funder: Engineering and Physical Sciences Research Council

Award: G6234512923

OpenAlex ID: W4408315865

FWCI: 1.924

Cites:

Cited by: 1

Related to: 10