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On the maximality conjecture for quantum permutation groups

Primarily AI-generated textHuman understanding: some partsmath.QA — Quantum Algebramath.OA — Operator Algebras

Contributed by Teo Banica ↗

Version 1 / Nov 02, 2026 / CC BY 4.0

Abstract

A well-known conjecture, central in quantum permutation group theory, and going back to around 2006, states that SN⊂SN+S_N\subset S_N^+ is maximal. We revisit here this conjecture, and related questions, 20 years after, with 2026 knowledge and tools.

Provenance statement

Written by Claude Opus, with help from Teo Banica

Tools used

Anthropic
Claude Opus

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Version history

  1. v1Submitted by Teo BanicaInitial depositCurrentNov 01, 2026