> If one is trying to prove a Hilbert space identity or inequality which is invariant under a unitary group action, one can often reduce "for free" to the irred

> If one is trying to prove a Hilbert space identity or inequality which is invariant under a unitary group action, one can often reduce "for free" to the irreducible components of that group action. This is really, really cool. I love a good unifying principle. Also this sort of "bag of tricks" comes in very handy. It's a lot like the analogous tricks and idioms in programming. You don't have to rediscover it from first principles, if you remember that exists while solving a problem.