群的表示与群的特征（第2版）

Representationtheoryisconcernedwiththewaysofwritingagroupasagroupofmatrices.Notonlyisthetheorybeautifulinitsownright，butitalsoprovidesoneofthekeystoaproperunderstandingoffinitegroups.Forexample，itisoftenvitaltohaveaconcretedescriptionofaparticulargroup；thisisachievedbyfindingarepresentationofthegroupasagroupofmatrices.Moreover，bystudyingthedifferentrepresentationsofthegroup，itispossibletoproveresultswhichlieoutsidetheframeworkofrepresentationtheory.Onesimpleexample：allgroupsoforderp2（wherepisaprimenumber）areabelian；thiscanbeshownquicklyusingonlygrouptheory，butitisalsoaconsequenceofbasicresultsaboutrepresentations.