The formulator of this statement used it to prove his namesake orthogonality relations, which makes this lemma a basic tenet of representation theory. For 10 points each:
[10h] Name this statement that implies that linear maps between certain finite representations of a group that commute with the action of the group are either isomorphisms or trivial.
ANSWER: Schur’s lemma
[10m] Schur’s lemma specifically applies to representations described by this adjective. Polynomials described by this adjective can not be factored into polynomials of a lower degree.
ANSWER: irreducible [accept irreducible representations or irreps; accept irreducible polynomials; accept not reducible]
[10e] The standard proof of Schur’s lemma begins by showing that the kernel of a linear map must be zero or the entirety of this set. A function maps this set to its range.
ANSWER: domain [prompt on inputs]
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