#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:
public/combinat/15361-branching- | 5feebdbfa73f64dafe28a5e4fe0144ab36083ab0
rules | Stopgaps:
Dependencies: |
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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 following rules are not implemented yet. The goal of this ticket 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.
>
> Another improvement that can be made now is to give a better method of
> concatenating branching rules. This is needed for branching to subgroups
> that are not maximal. Currently it can be done but is too cumbersome.
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 following rules are not implemented yet. The goal of this ticket 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
}}}
Another improvement that can be made now is to give a better method of
concatenating branching rules. This is needed for branching to subgroups
that are not maximal. Currently it can be done but is too cumbersome.
--
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Ticket URL: <http://trac.sagemath.org/ticket/15361#comment:7>
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