Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 210-02. Quadratic stabilization of the canonical Foulkes–Howe map
Manuscript map · lines 6145–6154
OpenAI@2026-10-07#rem:oai-p-210-02
Authors: OpenAI. Family 210.
Title: Quadratic stabilization of the canonical Foulkes–Howe map.
Abstract: For every finite-dimensional complex vector space V, we prove that the canonical Foulkes–Howe map ${}mathop{{}mathrm{Sym}}{}nolimits {}b({}mathop{{}mathrm{Sym}}{}nolimits {}a V){}longrightarrow{}mathop{{}mathrm{Sym}}{}nolimits {}a({}mathop{{}mathrm{Sym}}{}nolimits {}b V)$ is surjective whenever a ≥ 2 and $b{}ge a(a-1)$. This gives a quadratic stabilization bound independent of ${}dim V$.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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