nucleation

LIT-329: Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe

1 min read

Properties7
StatusActive — read in full 2026-09-29 (NOTE-305); worth reading as the primary source of the Peter–Weyl theorem, and it is short and constructive. Its setting is compact *Lie* groups and continuous functions. For arbitrary compact groups and the L²(G) = ⊕ (dim π)·π decomposition in modern form, a textbook statement (e.g. Weil 1940, or Folland's *A Course in Abstract Harmonic Analysis*) supersedes it.
Version2
Tagsmathematics
SupportsCLAIM-385 — If a symmetric operator on ℝⁿ commutes with an orthogonal representation of a compact group, each eigenspace is a sum of real irreducibles and each multiplicity a sum of multiples of their dimensions, so SO(2) and ℤ/n for n ≥ 3 force paired eigenvalues; conversely the spectrum fixes neither the group nor a basis inside an eigenspace
Cited as “grounds” byCLAIM-132 — Characters classify finite-dimensional representations of a finite or compact group up to isomorphism only over a field of characteristic zero; they forget the isomorphisms, fix neither the group nor a permutation action, and classify kinds, not tokens or positions
Cited as “paper” byNOTE-305 — Die Vollständigkeit der primitiven Darstellungen einer geschlossenen kontinuierlichen Gruppe
Cited as “source” byTHEORY-019 — Symmetry forces spectral degeneracy but degeneracy does not identify a symmetry: an operator commuting with a group has eigenspaces built from its real irreducibles, so abelian rotation groups force pairs over ℝ, and the spectrum fixes neither the group nor a basis inside a multiplet

Graph View

F. Peter, H. Weyl (1927), Mathematische Annalen 97:737–755 — DOI-10.1007/BF01447892

Standing in the record

Registered on 2026-09-29 at the owner’s request, because the owner’s prior-art novelty map (a private working document on concepts as projectors, the linear representation hypothesis and their neighbours) cites it: row 7: predicate harmonics = characters; irrep multiplets = spectral degeneracies. It is seeded from metadata and published descriptions and has not been read here.

Identification notes: Program name; canonical primary unambiguous. Nucleation holds a different Weyl work (LIT-108, Philosophy of Mathematics and Natural Science) — not this.

It was filed Deferred, unread. NOTE-305 is the close reading of 2026-09-29, and it placed the work: Active — worth reading as the primary source of the Peter–Weyl theorem, and it is short and constructive. Its setting is compact Lie groups and continuous functions. For arbitrary compact groups and the L²(G) = ⊕ (dim π)·π decomposition in modern form, a textbook statement (e.g. Weil 1940, or Folland’s A Course in Abstract Harmonic Analysis) supersedes it.

Backlinks