#15361: Branching Rules for Exceptional Groups
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Reporter: bump | Owner:
Type: PLEASE CHANGE | Status: new
Priority: major | Milestone: sage-6.0
Component: combinatorics | Keywords:
Merged in: | Authors: bump
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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Branching rules for Lie groups are mostly already implemented in
{{{weyl_characters}}}. That is, if G is a Lie group and H a subgroup
(maximal without loss of generality) we can compute the branching rule
from {{{G => H}}} in most cases, always if G is of classical type, and
sometimes if G is an exceptional group.
The branching rule {{{F4 => B4}}} seems to be broken. One purpose of this
ticket is to fix this.
The following rules are not implemented yet. The other purpose of these is
to implement the four
rules {{{G => G2 x H}}} where {{{G=F4,E6,E7,E8}}} and {{{H=A1,A2,C2,F4}}}.
The remaining 15 unimplemented may be implemented in later tickets.
{{{
E6 => C4 , A2 , G2 , A2xG2
E7 => A2 , A1 , A1 , A1xF4 , G2xC3 , A1xG2 , A1xA1
E8 => G2xF4 , C7 , A1xA2 , A1 , A1 , A1
F4 => A1 , A1xG2
}}}
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Ticket URL: <http://trac.sagemath.org/ticket/15361>
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