#5794: [with patch, needs review] G2 branching rules
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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):
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.
--
Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/5794#comment:3>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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