Let ρ:GGL(V) be a finite dimensional representation of a group G (i.e., V is a finite dimensional vector spaceMathworldPlanetmath over its scalar field K). The characterPlanetmathPlanetmath of ρ is the function χV:GK defined by


where Tr is the trace function.


  • χV(g)=χV(h) if g is conjugatePlanetmathPlanetmath to h in G. (Equivalently, a character is a class function on G.)

  • If G is finite, the characters of the irreducible representations of G over the complex numbers form a basis of the vector space of all class functions on G (with pointwise addition and scalar multiplication).

  • Over the complex numbers, the characters of the irreducible representations of G are orthonormal under the inner product

Title character
Canonical name Character
Date of creation 2013-03-22 12:17:54
Last modified on 2013-03-22 12:17:54
Owner djao (24)
Last modified by djao (24)
Numerical id 7
Author djao (24)
Entry type Definition
Classification msc 20C99