Template:Character table facts to check against: Difference between revisions

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{{quotation|'''FACTS TO CHECK AGAINST FOR CHARACTERS OF IRREDUCIBLE REPRESENTATIONS OVER SPLITTING FIELD''':<br>'''Orthogonality relations''': [[Character orthogonality theorem]] <nowiki>|</nowiki> [[Column orthogonality theorem]] <nowiki>|</nowiki> [[Splitting implies characters span class functions]] <br>'''Separation results''' (basically says any two rows distinct, any two columns distinct): [[splitting implies character-separating]] <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> [[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]] <nowiki>|</nowiki> [[Splitting implies characters span class functions]] <br>'''Separation results''' (basically says any two rows distinct, any two columns distinct): [[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> [[Zero-or-scalar lemma]]}}

Revision as of 02:04, 13 July 2011

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 functions
Separation results (basically says any two rows distinct, any two columns distinct): Character determines representation in characteristic zero
Numerical 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

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