Timeline for Irreducible representation of $S_n$: contained in tensor powers of the standard representation?
Current License: CC BY-SA 4.0
4 events
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| Jul 31, 2020 at 19:34 | comment | added | Will Sawin | @LSpice Suppose there is a copy of the sign representation in the tensor product. Take a generator (or the generator, since it's unique up to scaling). Write it in a basis of tensors of basis elements. Find one tensor of basis elements which has a nonzero coefficient. Since only $n-2$ basis elements can appear, two don't. Swap those and derive a contradiction. | |
| Jul 31, 2020 at 19:30 | history | edited | LSpice | CC BY-SA 4.0 |
Multiple $$ $$ -> align*
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| Jul 31, 2020 at 19:25 | comment | added | LSpice | Sorry for the silly question—why does the sign representation prevent going lower than $n - 1$? | |
| Jul 31, 2020 at 18:56 | history | answered | Will Sawin | CC BY-SA 4.0 |