Invariant Spinors on Flag Manifolds

Published 11 Jul 2024 in math.DG and math.RT | (2407.08493v2)

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.

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