Opened 13 years ago

Last modified 6 years ago

#5794 closed enhancement

[with patch, needs review] exceptional and reducible type branching rules — at Version 17

Reported by: bump Owned by: bump
Priority: major Milestone: sage-4.3
Component: group theory Keywords: lie groups
Cc: sage-combinat Merged in:
Authors: Reviewers:
Report Upstream: N/A Work issues:
Branch: Commit:
Dependencies: Stopgaps:

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Description (last modified by bump)

Patch summary for trac_5794.revised:

- new branching rules, including exceptional and reducible types
- all new rules have tests but slower F4 tests are # long time
- bugfix: reducible root system methods simple_roots etc. return families
- Cartan Types B, C and D allow low rank cases such as D2, B1 and C1
- WeylCharacterRings: new style="coroots" option gives output similar to published tables
- WeylCharacterRings: methods for rank, simple_roots etc.
- doc revision in weyl_characters.py

This patch contains #5831. If this patch is merged, that ticket may be closed.

The patch trac_5794-continued.patch goes on top of trac_5794-revised.patch. Together, the two patches give complete coverage of branching rules from classical root systems to maximal subgroups.

Highlights of the second patch:

New WeylCharacter methods is_reducible and frobenius_schur_indicator
Revised tensor rule handles all classical Cartan types
powerful new branching_rule_from_plethysm handles unusual cases
doc revision

The file at http://sporadic.stanford.edu/bump/branch.sage contains additional tests demonstrating every branching rule in Patera and McKay?'s book of tables for Cartan types A,B,C,D. This verifies the completeness of the patch for nonexceptional types.

The patch trac_5794-exceptional.patch adds some more F4 and E6 branching rules. It also adds dynkin_diagram and extended_dynkin_diagram methods to WeylCharacterRings?. It goes on top of the other two patches.

The last patch trac_5794-more-exceptional.patch adds E6, E7 and E8 branching rules.

Change History (21)

comment:1 Changed 13 years ago by bump

  • Cc sage-combinat added
  • Component changed from algebra to group_theory
  • Keywords lie groups added
  • Owner changed from tbd to joyner

comment:2 Changed 13 years ago by bump

The last change indicates that I changed the owner from tbd to joyner. I don't remember doing that, and I don't see how I could have done it accidentally. Maybe someone else changed the owner, presumably wdj or mabshoff, but then trac shouldn't show that I did. I am puzzled by this.

Here are some comments about the G2=>A1 Levi branching rule. There is a branching rule G2=>A1xA1 (rule = "extended"). This is not implemented yet. Currently Weyl character rings are broke for reducible root systems. (I have a patch for that but it is not posted on trac yet.) I intend to implement branching to reducible root systems but first I want to do a few exceptional branching rules first before tackling the *many* cases of branching to reducible root systems.

So G2=>A1xA1 will come in a later patch but it is relevant here so I will discuss it.

In the branching rule G2=>A1xA1, the second A1 is almost but not quite the A1 in the G2=>A1 Levi branching rule. (The short root A1.) So it might seem that one should implement G2=>A1xA1 and then you would get the G2=>A1 (rule = "levi") branching rule. However this is not quite true. The A1 in the G2=>A1 branching rule is GL(2) and the A1 in A1xA1 is SL(2).

comment:3 Changed 13 years ago by bump

I uploaded a second patch trac_5794-f4.patch which goes on top of the first. It implements branching rules F4=>B3 (levi), F4=>C3 (levi) and F4=>B4 (extended).

There is another extended rule F4=>C3xA1 (not implemented yet, but hopefully to be implemented later).

In contrast with G2, for F4, both Levi branching rules are redundant since the Levi subgroups are not maximal. They factor through branching rules F4=>B4=>B3 and F4=>C3xA1=>C3. However I implemented them for convenience. You can check directly that F4(x).branch(B3,rule="levi") and F4(x).branch(B4,rule="extended").branch(B3,rule="levi") return the same thing for x in F4.fundamental_weights().

I compared the output for these rules against those that I could find in a book, Patera and Sankoff, Branching rules for representations of simple Lie algebras.

comment:4 Changed 13 years ago by bump

  • Summary changed from [with patch, needs review] G2 branching rules to [with patch, needs review] G2 and F4 branching rules

comment:5 Changed 13 years ago by bump

  • Description modified (diff)

comment:6 Changed 13 years ago by bump

  • Description modified (diff)

comment:7 Changed 13 years ago by mabshoff

Hi Dan,

the change in ownership happend because you changed the component to "group_thoery". For every ticket you work on and post patches you should accept it (see the bottom left), that way ownership stays with you.

Cheers,

Michael

comment:8 Changed 13 years ago by bump

  • Owner changed from joyner to bump
  • Status changed from new to assigned

comment:9 Changed 13 years ago by bump

  • Description modified (diff)
  • Summary changed from [with patch, needs review] G2 and F4 branching rules to [with patch, needs review] exceptional and reducible type branching rules

Changed 13 years ago by bump

comment:10 Changed 13 years ago by bump

  • Milestone changed from sage-combinat to sage-4.0

I'm taking the liberty of changing the milestone to 4.0 in case there is a chance of getting this merged. It is quite a substantial enhancement.

comment:11 Changed 13 years ago by bump

Here are some tests supplementing those implemented in the doctests:

http://sporadic.stanford.edu/bump/branch.sage

Changed 13 years ago by bump

comment:12 Changed 13 years ago by bump

  • Description modified (diff)

comment:13 Changed 13 years ago by bump

Is it possible to remove the first two patches:

trac_5794.patch
trac_5794-f4.patch

They are superceded by the other patches. I am going to be adding some more patches to this series, and I think it would be less confusing if the first two patches are removed. I don't think I can do this without help from admin.

Dan

Changed 13 years ago by bump

comment:14 Changed 13 years ago by bump

  • Description modified (diff)

comment:15 Changed 13 years ago by bump

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comment:16 Changed 13 years ago by bump

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Changed 13 years ago by bump

comment:17 Changed 13 years ago by bump

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