Algebra · Result 204

Tensor saturation for even spin groups

1 paper

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.

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Papers 1

Tensor saturation for even spin groups

OpenAI · 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.

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Cite

@misc{OAI:Tensor-Saturation-for-Even-Spin-Groups-September-24-2026,
  author = {{OpenAI}},
  title = {{Tensor saturation for even spin groups}},
  howpublished = {OpenAI Math Release preprint
                  \href{https://github.com/openai/math/blob/main/preprints/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026/Tensor-Saturation-for-Even-Spin-Groups-September-24-2026.pdf}{OAI:Tensor-Saturation-for-Even-Spin-Groups-September-24-2026}},
  year = {2026}
}

Formal verification

No Lean formalization is listed for this result yet. The repository notes that unformalized results could have issues.