Sn = symmetric group
For each p in Sn associate a +1(p even) or -1(p odd)
a group algebra can be defined on the elements of Sn.
Theorem: The number of standard young tableau corresponding to a particular young diagram = dim of associated irrep denoted by the diagram.
Sn has the general symmetry elements built from the symmetrizer, antisymmetrizer, and young diagrams.
Define a general symmetry as:
Yl,q=Sl,q*Al,q
where l = the particular young diagram, q= the particular numbering of the
young diagram, Sl,q= symmetry on the rows, and Al,q=antisymmetry on the
columns.
Example:
1 2
3
=(e+12)(e-13)
12
34
= (e+(12))(e+(34))(e-(13))(e-(24))