Opened 4 years ago

Closed 4 years ago

#26112 closed enhancement (fixed)

Implement finite complex reflection groups G(m,p,n) as permutation groups

Reported by: tscrim Owned by:
Priority: major Milestone: sage-8.6
Component: group theory Keywords: complex reflection group
Cc: stumpc5 Merged in:
Authors: Travis Scrimshaw Reviewers: Frédéric Chapoton
Report Upstream: N/A Work issues:
Branch: 890c53b (Commits, GitHub, GitLab) Commit: 890c53b47c54b94ecfc7bc5fb5c92c6db86c5392
Dependencies: Stopgaps:

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Description

We can use an m-copy folding of Sn plus a connector to obtain G(m,1,n) and then an embedding of G(m,p,n) into G(m,1,n) to construct these groups as permutation groups.

Change History (13)

comment:1 Changed 4 years ago by tscrim

  • Branch set to public/group_theory/complex_refl_gp_perm_gp-26112
  • Commit set to 4378d9a0c80014be19be4bba03bb3dddeea824fc
  • Status changed from new to needs_review

New commits:

4378d9aImplementing G(m,p,n) as a permutation group.

comment:2 Changed 4 years ago by chapoton

sage -t --long src/sage/combinat/colored_permutations.py
**********************************************************************
File "src/sage/combinat/colored_permutations.py", line 636, in sage.combinat.colored_permutations.ColoredPermutations.as_permutation_group
Failed example:
    C.as_permutation_group()
Expected:
    Permutation Group with generators [(2,3)(5,6)(8,9)(11,12), (1,2)(4,5)(7,8)(10,11), (1,4,7,10)]
Got:
    Complex reflection group G(4, 1, 3) as a permutation group

comment:3 Changed 4 years ago by git

  • Commit changed from 4378d9a0c80014be19be4bba03bb3dddeea824fc to 7934f2044f530d24b838b3b5dfb09842e523691b

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

7934f20Implementing G(m,p,n) as a permutation group.

comment:4 Changed 4 years ago by tscrim

Whoops, forgot to change that. Fixed.

comment:5 Changed 4 years ago by stumpc5

I am a little puzzles with this implementation. What is a complex reflection group for you?

By definition, it is a subgroup of GL(V) generated by complex reflections. For me, you implement subgroups of the group of colored permutations where the sums of the colors satisfy a certain divisibility.

Also, what about the exceptional complex reflection groups? Shouldn't an class called ComplexReflectionGroup be able to initiate any complex reflection group?

comment:6 Changed 4 years ago by git

  • Commit changed from 7934f2044f530d24b838b3b5dfb09842e523691b to 934c45bae26dcc569c05f20ef8de2c961106d661

Branch pushed to git repo; I updated commit sha1. New commits:

934c45bAdding exceptional CRGs to API but currently raises a NotImplementedError.

comment:7 Changed 4 years ago by git

  • Commit changed from 934c45bae26dcc569c05f20ef8de2c961106d661 to c6d8df2e908984452cec6286152bbe788f44b6a7

Branch pushed to git repo; I updated commit sha1. New commits:

c6d8df2A little bit more documentation.

comment:8 Changed 4 years ago by tscrim

I made it so the API for ComplexReflectionGroup explicitly declares it will one day be able to handle an exceptional CRG, but currently raises a NotImplementedError.

comment:9 Changed 4 years ago by chapoton

typo: The convenion

also there is a "degrees" in the doc of codegrees

Otherwise looks good

comment:10 Changed 4 years ago by git

  • Commit changed from c6d8df2e908984452cec6286152bbe788f44b6a7 to 890c53b47c54b94ecfc7bc5fb5c92c6db86c5392

Branch pushed to git repo; I updated commit sha1. New commits:

f4c35aeMerge branch 'public/group_theory/complex_refl_gp_perm_gp-26112' of git://trac.sagemath.org/sage into public/group_theory/complex_refl_gp_perm_gp-26112
890c53bFixing typos.

comment:11 Changed 4 years ago by tscrim

  • Milestone changed from sage-8.4 to sage-8.6

Fixed.

comment:12 Changed 4 years ago by chapoton

  • Reviewers set to Frédéric Chapoton
  • Status changed from needs_review to positive_review

ok, let it be

comment:13 Changed 4 years ago by vbraun

  • Branch changed from public/group_theory/complex_refl_gp_perm_gp-26112 to 890c53b47c54b94ecfc7bc5fb5c92c6db86c5392
  • Resolution set to fixed
  • Status changed from positive_review to closed
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