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Add functions to produce conformal groups #43

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fingolfin opened this issue Dec 4, 2023 · 1 comment
Open

Add functions to produce conformal groups #43

fingolfin opened this issue Dec 4, 2023 · 1 comment
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enhancement New feature or request

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@fingolfin
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After discussion with @aniemeyer and @danielrademacher we think it would be important to have constructors for conformal orthogonal groups. We could just add them to forms (say in lib/classical.gi). On the long run, perhaps these could also be added to GAP directly...

For this we need paper(s) describing generators for these. If anyone has information on that, please share.

It was suggested that perhaps https://www.maths.usyd.edu.au/u/don/code/Magma/CSpConjugacy.pdf or https://www.maths.usyd.edu.au/u/don/code/Magma/CGOConjugacy.pdf might be a good starting point

@ThomasBreuer might also be interested in this

@fingolfin
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Having a quick look at that source, it seems basically we need to "add in" a diagonal matrix of the form $\mathrm{diag}(a,\dots,a,1,\dots,1)$ where $a$ is a primitive root of the ground field (at least for orthogonal and symplectic groups; I didn't look for the unitary case yet).

@fingolfin fingolfin added the enhancement New feature or request label Oct 16, 2024
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