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Remove broken markdown from greenfunction tables #301

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SoongNoonien
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I looked through the greenfunction info strings again. The issues with the markdown are mostly related to the GreenFunctionsA and GreenFunctionsA2 functions from the original CHEVIE which are still missing in this project. I think when they are implemented here as well we should mention them at the docs separately and maybe readd them to the info strings of the tables I removed them from with this PR.

However one issue remains I'm not sure how to resolve. I don't understand the info string of 2D4n2. So, I'm struggling to translate it to valid markdown. @fingolfin Perhaps you know what the string means?

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codecov bot commented Jun 25, 2025

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All modified and coverable lines are covered by tests ✅

Project coverage is 95.10%. Comparing base (a044d8c) to head (5c49882).

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@@           Coverage Diff           @@
##           master     #301   +/-   ##
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  Coverage   95.10%   95.10%           
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  Files          14       14           
  Lines         961      961           
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  Misses         47       47           

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of $\mathrm{GL}_n(q)$ and $\mathrm{GU}_n(q)$ is part of the CHEVIE-system. You
can reproduce them with the CHEVIE commands:
> GreenFunctionsA(n,filename);
> GreenFunctions2A(n,filename);
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It would of course be nice if we also had these commands. Maybe open an issue for that?

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There already is :-) #218

@fingolfin
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2D4n2 has this:

- This table of generalized Green functions is computed by F. Lübeck
  using Lusztig's algorithm.`,`
- The occuring Levi subgroups have the following relative (twisted)
  Weyl groups:
      Levi L                           type of N(L)/L
[ [ D, 0 ] ]           [ [ D, 4, 2 ] ]

- Position [-1,-1] contains the transformation matrix to the
  Foulkes functions and [0,-1] the corresponding labels.

The first bullet point seems clear.

The second ... I think the Levi subgroup here is a torus (at least I think the [ [ D, 0 ] ] indicates that? I might be wrong, though). Anywya, $N(L)/L$ is the quotient of the normalizer of $L$ by $L$, and this is a (relative, twisted) Weyl group, and again I assume [ [ D, 4, 2 ] ] indicates its type, which just means $^2D_4$. I.e. a $D_4$ twisted by an involutory graph automorphism (this of course is consistent with the "2D4" in the filename)

The third bullet point I have no idea about.

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2 participants