PreprintCC BY 4.0arXiv
Tournaments, flags, and spinors
Abstract
It is observed that the dimension of the space of invariant spinors on the manifold SU(n)/Tn−1 of full flags in ℂn equals the number RT(n) of labelled regular tournaments of order n, for n odd. This space is decomposed under a double cover of the Weyl group, and realized as a pair of eigenspaces, first for the Dirac operator, then for a twisted version of it which acts equivariantly; this is used to show that multiplicities of irreducible representations are even for n≡ 1pmod 4.
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BibTeX
@misc{conti2026tournaments,
title = {{Tournaments, flags, and spinors}},
author = {Diego Conti and Simon Salamon},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18084},
eprint = {2610.18084},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18084},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Tournaments, flags, and spinors
AU - Diego Conti
AU - Simon Salamon
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18084
UR - https://arxiv.org/abs/2610.18084
AB - It is observed that the dimension of the space of invariant spinors on the manifold SU(n)/T^n−1 of full flags in ℂ^n equals the number RT(n) of labelled regular tournaments of order n, for n odd. This space is decomposed under a double cover of the Weyl group, and realized as a pair of eigenspaces, first for the Dirac operator, then for a twisted version of it which acts equivariantly; this is used to show that multiplicities of irreducible representations are even for n≡ 1pmod 4.
ER -