We study cluster structures on spinor helicity and momentum twistor varieties which describe the kinematic spaces of massless scattering (with or without dual conformal symmetry). Both are instances of partial flag varieties. We exhibit embeddings of the corresponding cluster algebras into cluster algebras of sufficiently large Grassmannians and show how the former is obtained from the latter by freezing certain cluster variables and specializing some cluster variables to one.
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Bossinger et al. (2024) studied this question.
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