Let be a group, and any finite set on which acts.
That means that for any ;
Then the action of in can be extended linearly to as
and then the map where is such that makes into a -module. The -module is known as the permutation representation associated with .
If acts on , then
If , the action becomes
References. Bruce E. Sagan. The Symmetric Group: Representations, Combinatorial Algorithms and Symmetric Functions. 2a Ed. 2000. Graduate Texts in Mathematics. Springer.
|Date of creation||2013-03-22 14:53:59|
|Last modified on||2013-03-22 14:53:59|
|Last modified by||drini (3)|