Timeline for Invariants of matrices (by simultaneous $\mathrm{GL}_n$ conjugation) over arbitrary rings
Current License: CC BY-SA 4.0
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| Aug 26 at 23:24 | vote | accept | stupid_question_bot | ||
| S Aug 26 at 18:59 | vote | accept | stupid_question_bot | ||
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| Sep 13, 2021 at 23:22 | history | edited | stupid_question_bot | CC BY-SA 4.0 |
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| Sep 13, 2021 at 23:21 | history | edited | Will Chen | CC BY-SA 4.0 |
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| Sep 13, 2021 at 19:54 | vote | accept | stupid_question_bot | ||
| S Aug 26 at 18:59 | |||||
| Sep 13, 2021 at 19:54 | answer | added | stupid_question_bot | timeline score: 6 | |
| Sep 8, 2021 at 14:02 | history | edited | stupid_question_bot | CC BY-SA 4.0 |
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| Sep 8, 2021 at 8:59 | answer | added | Wilberd van der Kallen | timeline score: 14 | |
| Sep 8, 2021 at 3:16 | history | edited | stupid_question_bot | CC BY-SA 4.0 |
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| Sep 7, 2021 at 7:35 | comment | added | Wilberd van der Kallen | It must be true because Donkin shows one has a good filtration over $\mathbb Z$. That implies base change for the group scheme invariants. Infinite fields are only needed when one wants to confuse a group $G(k)$ with the group scheme $G_k$. | |
| Sep 7, 2021 at 7:15 | comment | added | stupid_question_bot | @darijgrinberg They seem to cover the cases of $R = \mathbb{Z}$ or $R$ an infinite field (see their proof in $\S15.2$) | |
| Sep 7, 2021 at 7:14 | history | edited | stupid_question_bot |
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| Sep 7, 2021 at 4:33 | history | edited | YCor | CC BY-SA 4.0 |
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| Sep 7, 2021 at 4:13 | comment | added | user44191 | It might be worth adding the [quivers] tag, as this is asking about the invariants for the one-vertex, d-loop quiver. | |
| Sep 7, 2021 at 3:02 | history | edited | stupid_question_bot | CC BY-SA 4.0 |
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| Sep 7, 2021 at 2:22 | history | edited | stupid_question_bot | CC BY-SA 4.0 |
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| Sep 7, 2021 at 2:14 | comment | added | stupid_question_bot | @LSpice The Sibirski result is cited in the introduction to Donkin's paper, though I have not checked it. Here's the citation: "Sibirski, K.S.: On unitary and orthogonal matrix invariants. Dokl. Akad. Nauk. SSSR 172, 1, 40-43 (1967)" | |
| Sep 7, 2021 at 1:50 | comment | added | darij grinberg | FWIW: This is also part of Theorem 1.10 in Corrado De Concini, Claudio Procesi, The Invariant Theory of Matrices, AMS 2017. But I'm not quite sure what they require of the base ring $R$; possibly it has to be a field. (But algebraic closedness can certainly not be useful; the claim is of the form "a vector lies in the span of a bunch of other vectors", so must hold in any prime field if it holds in an extension.) | |
| Sep 6, 2021 at 23:57 | comment | added | LSpice | Could you give a reference to the classical result? MathSciNet does not seem to recognise Sibirski. | |
| Sep 6, 2021 at 23:57 | history | edited | LSpice | CC BY-SA 4.0 |
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| Sep 6, 2021 at 23:31 | history | asked | stupid_question_bot | CC BY-SA 4.0 |