example of induced representation
To understand the definition of induced representation, let us work through a simple example in detail.
Since has half as many elements as , there are exactly two cosets, and in where
We will now compute the action of on this vector space. To do this, we need a choice of coset representatives. Let us choose as a representative of and as a representative of . As a preliminary step, we shall express the product of every element of with a coset representative as the product of a coset representative and an element of .
We will now compute of the action of using the formula given in the definition.
Here the square brackets indicate the coset to which the group element inside the brackets belongs. For instance, since .
The results of the calculation may be easier understood when expressed in matrix form
Having expressed the answer thus, it is not hard to verify that this is indeed a representation of . For instance, and
|Title||example of induced representation|
|Date of creation||2013-03-22 14:35:43|
|Last modified on||2013-03-22 14:35:43|
|Last modified by||rspuzio (6075)|