# 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 theorem | Splitting implies characters span class functionsSeparation results(basically says any two rows distinct, any two columns distinct): splitting implies character-separatingNumerical 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 | Zero-or-scalar lemma