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Packet M: Bonus 5

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]
<OSU A, Other Science> | Packet M - Columbia A, Ohio State A, Maryland A, Toronto C, Clemson A, Notre Dame A

HeardPPBE %M %H %
4916.3396%53%14%

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Conversion

TeamOpponentPart 1Part 2Part 3TotalParts
Chicago CChicago A0101020ME
Chicago DChicago B10101030HME
Illinois AIllinois C0101020ME
Indiana ANorthwestern B10101030HME
Indiana BChicago E001010E
Northwestern CPurdue B001010E
Northwestern DNotre Dame B001010E
Purdue AIllinois B0101020ME

Summary

TournamentEditionMatchHeardPPBE %M %H %
California (South)Main Site✓420.00100%75%25%
CanadaMain Site✓1017.0090%60%20%
Lower Mid-AtlanticMain Site✓110.00100%0%0%
Lower Mid-AtlanticMain Site✓611.67100%17%0%
MidwestMain Site✓818.75100%63%25%
NortheastMain Site✓514.00100%40%0%
OverflowMain Site✓313.33100%33%0%
UKMain Site✓1217.5092%67%17%