#5794: [with patch, needs review] G2 branching rules
--------------------------+-------------------------------------------------
Reporter: bump | Owner: joyner
Type: enhancement | Status: new
Priority: major | Milestone: sage-combinat
Component: group_theory | Keywords: lie groups
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Comment(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).
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5794#comment:2>
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