Supplementary Material 7 Elements of Group and Representation Theory

X , ( g,x ) 7! g.x which satisfies the axioms: identity: 8 x 2X e.x = x compatibility: 8 a, b 2 G 8 x 2X a. ( b.x )=( ab ) .x Given a signal x : G ! R , the action of an element g 2 G maps x 7! g.x, [ g.x ]( h ): = x ( g Maschke's theorem can be generalized to compact groups.