典型群

Eversincetheyear1925，whenIsucceededindeterminingthecharactersofthesemi-simplecontinuousgroupsbyacombinationofE.Cartansinfini-tesimalmethodsandI.Schursintegralprocedure，Ihavelookedtowardthegoalofderivingthedecisiveresultsforthemostimportantofthesegroupsbydirectalgebraicconstruction，inparticularforthefullgroupofallnon-singu-larlineartransformationsandfortheorthogonalgroup.OwingmainlytoR.Brauersinterventionandcollaborationduringthelastfewyears，itnowappearsthatIhaveinmyhandsallthetoolsnecessaryforthispurpose.Thetaskmaybecharacterizedpreciselyasfollows：withrespecttotheassignedgroupoflineartransformationsintheunderlyingvectorspace，todecomposethespaceoftensorsofgivenrankintoitsirreducibleinvariantsubspaces.