regular representation

Given a group G, the regular representationPlanetmathPlanetmath of G over a field K is the representationPlanetmathPlanetmath ρ:GGL(KG) whose underlying vector spaceMathworldPlanetmath KG is the K–vector space of formal linear combinationsMathworldPlanetmath of elements of G, defined by


for kiK, g,giG.

Equivalently, the regular representation is the induced representationMathworldPlanetmath on G of the trivial representation on the subgroupMathworldPlanetmathPlanetmath {1} of G.

Title regular representation
Canonical name RegularRepresentation
Date of creation 2013-03-22 12:17:40
Last modified on 2013-03-22 12:17:40
Owner djao (24)
Last modified by djao (24)
Numerical id 5
Author djao (24)
Entry type Definition
Classification msc 20C99