What question did this study set out to answer?

The aim is to establish the topological Noetherianity of infinite half-spin representations and introduce half-spin varieties.

February 26, 2026Open Access

Topological Noetherianity of the infinite half-spin representations

Key Points

The aim is to establish the topological Noetherianity of infinite half-spin representations and introduce half-spin varieties.
Proved topological Noetherianity for infinite half-spin representations
Introduced half-spin varieties
Determined defining equations for the infinite isotropic Grassmannian in its spinor embedding.
Half-spin varieties are defined by equations at a finite level
Explicit defining equations for the infinite isotropic Grassmannian were determined

Abstract

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.

Topological Noetherianity of the infinite half-spin representations

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Abstract

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