Character Theory

The character theory machinery is currently restricted to characters defined over the complex field.

• Definition of class functions
• Construction of permutation characters
• Arithmetic on class functions: sum, difference, tensor product
• Frobenius-Schur indicator
• Norm, order, kernel, centre of a character
• Properties: generalized character, character, irreducible, faithful, linear
• Induction and restriction of a character
• Decomposition of a tensor power: orthogonal components, symmetric components
• Action of a group on the characters of a normal subgroup
• Decomposition of characters
• Class matrix, structure constants for centre of group algebra
• Table of ordinary irreducible characters (Dixon-Schneider algorithm)