Today’s topic was originally the Schur orthogonality relations, chosen by Kevin T at Westwood HS. Just for context: Kevin is a 4-time USAMO qualifier (and counting).
Now I, just like the majority of my non-mathematician readers, know nothing about the Schur orthogonality relations, and the wiki article doesn’t seem to make it much clearer.
Kevin, would you like to explain this yourself?
A Reasoner's Miscellany 