regular representation
Given a group G, the regular representation of G over a field K is the representation
ρ:G⟶GL(KG) whose underlying vector space
KG is the K–vector space of formal linear combinations
of elements of G, defined by
ρ(g)(n∑i=1kigi):= |
for , .
Equivalently, the regular representation is the induced representation on of the trivial representation on the subgroup
of .
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 |