Tensor saturation for even spin groups

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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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The paper states

Theorem 1.1 (Type-D saturation)

In Tensor saturation for even spin groups, 24 September 2026

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Let G=\Spin(2n), n\ge2, and let \lambda,\mu,\nu be dominant integral weights such that \lambda+\mu+\nu\in Q(D_n). Then, for every positive integer N,

\bigl(V(\lambda)\otimes V(\mu)\otimes V(\nu)\bigr)^G\ne0 \quad\Longleftrightarrow\quad \bigl(V(N\lambda)\otimes V(N\mu)\otimes V(N\nu)\bigr)^G\ne0.

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Tensor saturation for even spin groups

24 September 2026, current edition.

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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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37 references in Tensor saturation for even spin groups

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