Invariant Spinors on Flag Manifolds
Differential Geometry
2025-09-19 v2 Representation Theory
Abstract
In this note, we characterise the existence of non-trivial invariant spinors on maximal flag manifolds associated to complex simple Lie algebras. This characterisation is based on the combinatorial properties of their set of positive roots. We also give some bounds for the dimension of the space of invariant spinors in each case.
Cite
@article{arxiv.2407.08493,
title = {Invariant Spinors on Flag Manifolds},
author = {Diego Artacho and Uwe Semmelmann},
journal= {arXiv preprint arXiv:2407.08493},
year = {2025}
}
Comments
10 pages. To apppear in the International Journal of Mathematics