#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 | Resolution:
Keywords: | Merged in:
Authors: bump | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
Dependencies: | Stopgaps:
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Description changed by bump:
Old description:
> 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
> }}}
New description:
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
}}}
Some doctests in {{{weyl_characters}}} are marked "long time" with
obsolete timing information. For example the doctest
{{{[F4(fw).branch(B3,rule="levi") for fw in F4.fundamental_weights()]}}}
is given with the timing information 36s. This takes less than a second on
my laptop.
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Ticket URL: <http://trac.sagemath.org/ticket/15361#comment:1>
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