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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
Brandeis AHarvard B001010E
Brandeis BMIT0101020ME
Harvard ABowdoin A0101020ME
Southern Connecticut StateBowdoin B001010E
YaleBrown001010E

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%