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
| Heard | PPB | E % | M % | H % |
|---|---|---|---|---|
| 49 | 16.33 | 96% | 53% | 14% |
Conversion
| Team | Opponent | Part 1 | Part 2 | Part 3 | Total | Parts |
|---|---|---|---|---|---|---|
| Brock | Toronto D | 0 | 0 | 10 | 10 | E |
| McGill B | UBC A | 0 | 0 | 10 | 10 | E |
| McMaster A | Guelph | 0 | 0 | 10 | 10 | E |
| Ottawa | UBC B | 10 | 10 | 10 | 30 | HME |
| Simon Fraser | Toronto E | 10 | 10 | 10 | 30 | HME |
| Toronto B | Queen's | 0 | 10 | 10 | 20 | ME |
| Toronto G | Western B | 0 | 10 | 10 | 20 | ME |
| Toronto Metropolitan | Carleton University | 0 | 0 | 0 | 0 | |
| Waterloo A | McGill A | 0 | 10 | 10 | 20 | ME |
| Waterloo B | Toronto F | 0 | 10 | 10 | 20 | ME |
Summary
| Tournament | Edition | Match | Heard | PPB | E % | M % | H % |
|---|---|---|---|---|---|---|---|
| California (South) | Main Site | ✓ | 4 | 20.00 | 100% | 75% | 25% |
| Canada | Main Site | ✓ | 10 | 17.00 | 90% | 60% | 20% |
| Lower Mid-Atlantic | Main Site | ✓ | 1 | 10.00 | 100% | 0% | 0% |
| Lower Mid-Atlantic | Main Site | ✓ | 6 | 11.67 | 100% | 17% | 0% |
| Midwest | Main Site | ✓ | 8 | 18.75 | 100% | 63% | 25% |
| Northeast | Main Site | ✓ | 5 | 14.00 | 100% | 40% | 0% |
| Overflow | Main Site | ✓ | 3 | 13.33 | 100% | 33% | 0% |
| UK | Main Site | ✓ | 12 | 17.50 | 92% | 67% | 17% |