Tensor saturation for even spin groups

Proves saturation factor one for \mathop{\mathrm{Spin}}\nolimits (2n), n ≥ 2: for three dominant integral weights whose sum lies in the root lattice, an invariant at any common positive integral dilation already gives an invariant at the original weights. This resolves the type-D part of the simply-laced saturation conjecture.

Manuscript

Tensor saturation for even spin groups

September 24, 2026 · source · cite as \cite{OAI:Tensor-Saturation-for-Even-Spin-Groups-September-24-2026}

We prove the saturation conjecture for \mathop{\mathrm{Spin}}\nolimits (2n), n ≥ 2. If three dominant integral weights sum to an element of the root lattice, then the existence of a nonzero tensor invariant after a positive integral dilation implies the existence of one at the original weights.

Result 204 · Algebra. Imported from openai/math, a collection of manuscripts produced by an OpenAI model; results are at different stages of verification. Discussion below is by Lemma members.