Jean-Pierre Serre (1977), Linear Representations of Finite Groups, Graduate Texts in Mathematics, New York: Springer — DOI-10.1007/978-1-4684-9458-7
Key takeaways
Registered, not read. What follows is the standard content of the book as the record’s claim uses it, not checked against the text.
- Characters are complete in characteristic zero. For a finite group and finite-dimensional complex representations, every representation is a direct sum of irreducibles (Maschke), the irreducible characters are orthonormal for the usual inner product on class functions, and so a representation is fixed up to isomorphism by its character.
- The irreducible characters are a basis of the class functions, as many as there are conjugacy classes.
- Beyond characteristic zero the classification changes. Modular representations, where the characteristic divides the group order, are treated separately, and there characters alone do not classify.
Standing in the record
Registered on 2026-10-10 to ground CLAIM-132, the granted claim that characters classify kinds up to isomorphism only in characteristic zero. That claim bounds the owner’s U54 analogy between communicative kinds and group characters (CLAIM-137). The exchange stated the theorem correctly at A194 §1 and A198 §2 and cited no source the record could check.
Deferred because nobody here has read it. The results the claim uses were
checked by reasoning. A reading would check them against the book’s chapter
on character theory and its treatment of modular representations, and would
let the claim cite page and theorem.