# Difference between revisions of "Template:Character table facts to check against"

From Groupprops

Line 1: | Line 1: | ||

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

## Revision as of 17:05, 16 July 2011

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 integersCharacter value facts: | 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