HEXAGONbeta

On properties of Plancherel algebras

Primarily AI-generated textHuman understanding: some partsmath.AG — Algebraic Geometrymath.NT — Number Theorymath.RT — Representation Theory

Contributed by Shurui Liu ↗

SubmitterShurui Liu

Version 1 / Sep 30, 2026 / CC BY 4.0

Abstract

We proved the predictions by Ben-Zvi, Sakellaridis, and Venkatesh that the Plancherel algebra PLX\mathrm{PL}_{X} is commutative and its loop-rotated version PLX,ℏ\mathrm{PL}_{X,\hbar} is flat over k[ℏ]k[\hbar].

Provenance statement

The main body of this paper is generated by generative AI. The proof to commutativity of $\mathrm{PL}_X$ and the proof to flatness of $\mathrm{PL}_{X,\hbar}$ are autonomously generated by a math reasoning agent called Rethlas, enhanced by OSVerify, with base model GPT-6-Astra Max. The output is briefly reviewed by human and believed to be overall correct.

Tools used

OpenAI
CodexVersion GPT-6-Astra
Rethlas
https://github.com/frenzymath/RethlasVersion commit 887cc46427636bbdd235160a112f9a30ae81d040
OSVerify
OSVerify

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Version history

  1. v1Initial depositCurrentSep 29, 2026