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:

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.

source

jl@crush.caltech.edu index

standard_young_tableau

Sn

SU

SO