# Template:Character table facts to check against

FACTS TO CHECK AGAINST FOR CHARACTERS OF IRREDUCIBLE REPRESENTATIONS OVER SPLITTING FIELD:Orthogonality relations: Character orthogonality theorem | Column orthogonality theoremSeparation results(basically says rows independent, columns independent): Splitting implies characters form a basis for space of class functions|Character determines representation in characteristic zeroNumerical facts: Characters are cyclotomic integers | Size-degree-weighted characters are algebraic integers | Irreducible character of degree greater than one takes value zero on some conjugacy class | Conjugacy class of more than average size has character value zero for some irreducible character | Zero-or-scalar lemma