Timeline for Action of complex torus on a vector space
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jan 9, 2023 at 22:39 | vote | accept | prochet | ||
| Jan 9, 2023 at 20:48 | comment | added | LSpice | Your title asked for an action by the multiplicative group, but your body asked for an action by any complex torus; and you wrote the target of the representation as $\mathrm{GL}_n(V)$, but you almost certainly meant either $\operatorname{GL}_n(\mathbb C)$ or $\operatorname{GL}(V)$. I edited accordingly. (Also, re, as @DavidSpeyer indicates, without some compatibility requirement the result isn't true.) | |
| Jan 9, 2023 at 20:45 | history | edited | LSpice | CC BY-SA 4.0 |
Error in title; missing word
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| Jan 9, 2023 at 18:16 | history | edited | YCor | CC BY-SA 4.0 |
formatting
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| Jan 9, 2023 at 17:08 | answer | added | David E Speyer | timeline score: 8 | |
| Jan 5, 2023 at 20:09 | comment | added | prochet | First by a torus, I mean an algebraic torus, thus isomorphic to $(\mathbb{C}^{*})^{n}$. Also a priori it is not clear that the representation $\rho$ is compatible with complex conjugation or transposition. | |
| Jan 5, 2023 at 15:35 | comment | added | Nicholas Kuhn | Combine: (a) unitary matrices are diagonalizable, and (b) commuting diagonizable matrices are simultaneously diagonalizable. (a) is often taught and (b) is often an exercise in (high level) undergraduate courses. | |
| Jan 5, 2023 at 9:13 | history | asked | prochet | CC BY-SA 4.0 |