QUIGS Seminar: Representation Theory for Finite Groups (Symmetric Groups)

SPEAKERS:  Comfort Mintah and Matthew Kazakov

We review the basics of representation theory for the symmetric groups denoted by Sn. We will see that
every symmetric group can be decomposed into direct sums of irreducible representations. We use an
example to establish the character table for the case when n = 4 (the symmetric group S4) and then
write the direct sum decomposition for S4. Next, we illustrate the direct sum decomposition for S4 using
an alternative method(Young's Tableau). Finally, we give some useful applications of the representation
theory in Quantum Information, example Quantum Error Correction and Local Operations and Classical
Communication.