induced representation
Let G be a group, H⊂G a subgroup, and V a representation of H, considered as a ℤ[H]–module. The induced representation
of ρ on G, denoted IndGH(V), is the ℤ[G]–module whose underlying vector space
is the direct sum
⊕σ∈G/HσV |
of formal translates of V by left cosets
σ in G/H, and whose multiplication operation
is defined by choosing a set {gσ}σ∈G/H of coset representatives and setting
g(σv):= |
where is the unique left coset of containing (i.e., such that for some ).
One easily verifies that the representation is independent of the choice of coset representatives .
Title | induced representation |
---|---|
Canonical name | InducedRepresentation |
Date of creation | 2013-03-22 12:17:33 |
Last modified on | 2013-03-22 12:17:33 |
Owner | djao (24) |
Last modified by | djao (24) |
Numerical id | 4 |
Author | djao (24) |
Entry type | Definition |
Classification | msc 20C99 |