Tournaments, flags, and spinors

Diego Conti; Simon Salamon

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arXiv · 2610.18084

Tournaments, flags, and spinors

Diego Conti·Simon Salamon

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Abstract

It is observed that the dimension of the space of invariant spinors on the manifold $\mathrm{SU}(n)/T^{n-1}$ of full flags in $\mathbb{C}^n$ equals the number $\mathrm{RT}(n)$ 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 $n\equiv 1\pmod 4$.

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Diego Conti, Simon Salamon. 2026-10-13. Tournaments, flags, and spinors. https://arxiv.org/abs/2610.18084

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