#15361: Branching Rules for Exceptional Groups
-------------------------------------+-------------------------------------
Reporter: bump | Owner:
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.1
Component: combinatorics | Resolution:
Keywords: | Merged in:
Authors: bump | Reviewers:
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/combinat/15361-branching- | db39e9256986b10ffe67551215734dc33cc34c60
rules | Stopgaps:
Dependencies: |
-------------------------------------+-------------------------------------
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.
>
> Before the patch, the following rules are not implemented. The patch
> implements four of these, namely
> 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
> }}}
>
> The patch makes a class BranchingRule for branching rules. Notable
> methods are a multiplication
> corresponding to composition, and a {{{describe()}}} method for branching
> rules which shows how simple roots and the affine root restrict. The
> multiplication gives a better method of concatenating branching rules. A
> projection method for composite types is given. The thematic tutorial is
> revised. The goals set out in Comment 6 are all achieved except for the
> one about the Levi branching rule {{{E6 => A5}}}. However the patch makes
> this easy to implement as follows:
> {{{branching_rule("E6","A5xA1",rule="extended")*branching_rule("A5xA1","A5","proj1")}}}
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.
Before the patch, the following rules are not implemented. The patch
implements four of these, namely
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 , C2 , A1xA2 , A1 , A1 , A1
F4 => A1 , A1xG2
}}}
The patch makes a class BranchingRule for branching rules. Notable methods
are a multiplication
corresponding to composition, and a {{{describe()}}} method for branching
rules which shows how simple roots and the affine root restrict. The
multiplication gives a better method of concatenating branching rules. A
projection method for composite types is given. The thematic tutorial is
revised. The goals set out in Comment 6 are all achieved except for the
one about the Levi branching rule {{{E6 => A5}}}. However the patch makes
this easy to implement as follows:
{{{branching_rule("E6","A5xA1",rule="extended")*branching_rule("A5xA1","A5","proj1")}}}
--
--
Ticket URL: <http://trac.sagemath.org/ticket/15361#comment:33>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
and MATLAB
--
You received this message because you are subscribed to the Google Groups
"sage-trac" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to [email protected].
To post to this group, send email to [email protected].
Visit this group at http://groups.google.com/group/sage-trac.
For more options, visit https://groups.google.com/groups/opt_out.
