The Labelling of Irreducible Representations

All representations for single objects (nondegenerate) are designated either A or B. Doubly degenerate representations are given the symbol E and triply degenerate representations T. 

A representations have character 1 with respect to the principal axis primary operation, while B representations have character -1 for the principal axis. 

Subscripts 1 and 2 are attached to A and B labels to indicate those that are symmetric (subscript 1) and antisymmetric (subscript 2) with respect to a C2 axis perpendicular to the principal axis or, if the axis is absent, to a vertical mirror plane. Symmetric means a character +1 and antisymmetric a character of — 1. 

In groups with a centre of inversion i, the subscripts g and u are added to symbols of representations which are symmetric and antisymmetric respectively for the inversion operation. These symbols come from the German words gerade meaning even and mgerade meaning odd . 

Primes and double primes are attached to letters to indicate those that are symmetric and antisymmetric with respect to in groups that do not contain i. 

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