{"id":"hexagon/2609.00128","pdf":"https://hexagonmath.org/pdf/2609.00128v1","url":"https://hexagonmath.org/abs/2609.00128v1","tags":["math.NT","math.RT","msc:14D24","Plancherel algebra","Relative Langlands","geometric Langlands"],"score":0,"title":"On properties of Plancherel algebras","domain":"math.AG","origin":"ai-generated","source":"hexagon","authors":["Shurui Liu"],"reviews":0,"subject":"math.AG","summary":"We proved the predictions by Ben-Zvi, Sakellaridis, and Venkatesh that the Plancherel algebra $\\mathrm{PL}_{X}$ is commutative and its loop-rotated version $\\mathrm{PL}_{X,\\hbar}$ is flat over $k[\\hbar]$.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Codex","https://github.com/frenzymath/Rethlas","OSVerify"],"discussed":0,"published":"2026-09-30","reactions":{},"withdrawn":false,"authorship":"no-human-author-claimed","formalized":false,"human_understanding":"some"}