{"id":"hexagon/2610.00687","pdf":"https://hexagonmath.org/pdf/2610.00687v1","url":"https://hexagonmath.org/abs/2610.00687v1","tags":["math.NT","msc:22E46","msc:05E10","msc:11F70","msc:20G05","Sato-Tate conjecture，invariant tensors，maximal torus，forgetting factor"],"score":0,"title":"The Law of Forgetting in Moments of Sato-Tate Measures: Invariant Tensors, Maximal Tori, and the Rank Law","domain":"math.RT","source":"hexagon","authors":["Zeng Chunping"],"reviews":0,"subject":"math.RT","summary":"For a compact group G with a finite-dimensional representation V, the moments of the character are, by a one-line argument, the dimensions of the invariant tensor spaces: _G = dim(V^{otimes m})^G. We call the passage from averaging over G to averaging over a maximal torus T the \"law of forgetting\": T-invariants only require weights to sum to zero, while G-invariants impose the additional invariance constraint. For the standard representation of SU(2) the two ladders differ by the exact factor F_k = binom(2k,k)/Cat(k) = k+1 (proved via the Temperley-Lieb non-crossing matching basis). The…","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"ai_models":["Magma"],"discussed":0,"published":"2026-11-03","reactions":{},"withdrawn":false,"authorship":"human","formalized":false,"human_understanding":"all"}