Young diagrams with n boxes characterize the conjugacy classes of Sn.
=> irreps of Sn are also labeled by the Young diagrams.
length of row i = size of ith largest cycle in a conjugacy class of Sn.
A general young diagram is of the form:
#######
#####
##
#
The dimension of the diagram is:
Fill the diagram out in the following way:
m (m+1) (m+2)....
(m-1) m ...
.
.
.
And multiply everything together.
divide by:
form the same young tableau.
In each box put the number of boxes to the right + the number down +1.
multiply them all together.
= dimension of corresponding irrep.