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This research reveals the topological Noetherianity of half-spin varieties in relation to the infinite spin group, indicating their equations can be defined at finite levels.
We prove that the infinite half-spin representations are topologically Noetherian with respect to the infinite spin group. As a consequence, we obtain that half-spin varieties, which we introduce, are defined by the pullback of equations at a finite level. The main example for such varieties is the infinite isotropic Grassmannian in its spinor embedding, for which we explicitly determine its defining equations.
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Chiu et al. (2025) studied this question.
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