The Geometry of Generalised Spinr Spinors on Projective Spaces

被引：0
作者：
Artacho, Diego [1 ]
Hofmann, Jordan [2 ]
机构：
[1] Imperial Coll London, London SW7 2AZ, England
[2] Kings Coll London, London WC2R 2LS, England
来源：
SYMMETRY INTEGRABILITY AND GEOMETRY-METHODS AND APPLICATIONS | 2025年 / 21卷
基金：
英国工程与自然科学研究理事会;
关键词：
special spinors; projective spaces; generalized spin structures; spinc; spinh; KILLING SPINORS; PARALLEL; REPRESENTATION; EIGENVALUE; BUNDLES;
D O I：
10.3842/SIGMA.2025.017
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we adapt the characterisation of the spin representation via exterior forms to the generalised spinr context. We find new invariant spinr spinors on the projective spaces CPn, HPn, and the Cayley plane OP2 for all their homogeneous realisations. Specifically, for each of these realisations, we provide a complete description of the space of invariant spinr 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 spinr spinors on these spaces.
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页数：32
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