The Lipschitz Spinor-Higher Horosphere Correspondence

Abstract

In a paper of Mathews, an isomorphism is constructed between two-component complex spinors and horospheres in H^3 carrying `spin decorations'. A recent arXiv preprint of Mathews and Varsha arXiv:2412.06572 extends this result to the case of `quaternionic spinors' and spin decorated horospheres in H^4. The following work generalises these results to an equivariant correspondence between two-component `Lipschitz spinors' with entries drawn from the Lipschitz group of a Clifford algebra, null multiflags in generalised Minkowski space, and higher-dimensional horospheres that carry an extension of the Mathews spin decoration. This correspondence allows spinors to be applied to horospheres in any dimension of hyperbolic space.

73 pages, 2 figures, adapted from the author's thesis available at https://doi.org/10.26180/31361224