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Universality of high-strength tensors

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arxiv 2105.00016 v2 pith:HJJGGWFL submitted 2021-04-30 math.AG math.AC

Arthur Bik , Alessandro Danelon , Jan Draisma , Rob H. Eggermont This is my paper · ORCID
classification math.AGmath.AC
keywords polynomialelementsfunctorsquasi-ordertheoremvariablesarbitrarybounded
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A theorem due to Kazhdan and Ziegler implies that, by substituting linear forms for its variables, a homogeneous polynomial of sufficiently high strength specialises to any given polynomial of the same degree in a bounded number of variables. Using entirely different techniques, we extend this theorem to arbitrary polynomial functors. As a corollary of our work, we show that specialisation induces a quasi-order on elements in polynomial functors, and that among the elements with a dense orbit there are unique smallest and largest equivalence classes in this quasi-order.

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A remark on automorphisms of tensor spaces

    math.RT 2025-07 accept novelty 7.0 of 10

    Any graph automorphism group is realized as the automorphism group of a symmetric (3,2,2)-tensor space, and the paper constructs spaces where V is irreducible but V⊗2 has infinite length.

  2. The fundamental theorems of invariant theory for linearly oligomorphic groups

    math.RT 2026-07 accept novelty 6.0 of 10

    The G-invariant symmetric forms on V^m for the automorphism group G of a universal homogeneous λ-space are freely generated by the contractions of the defining forms with Schur functors on k^m.

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