Linear representation theory of alternating groups

This article discusses the linear representation theory of the alternating group $A_{n}$ of finite degree $n$. Note that for $n=0,1$, the alternating group coincides with the symmetric group, and for $n=2$, it is trivial, so the interesting behavior begins from $n=3$.

The article builds heavily on the linear representation theory of symmetric groups.

Particular cases

$n$	Alternating group	Order	Linear representation theory page
3	cyclic group:Z3	3	linear representation theory of cyclic group:Z3
4	alternating group:A4	12	linear representation theory of alternating group:A4
5	alternating group:A5	60	linear representation theory of alternating group:A5
6	alternating group:A6	360	linear representation theory of alternating group:A6
7	alternating group:A7	2520	linear representation theory of alternating group:A7
8	alternating group:A8	20160	linear representation theory of alternating group:A8
9	alternating group:A9	181440	linear representation theory of alternating group:A9
10	alternating group:A10	1814400	linear representation theory of alternating group:A10