#15361: Branching Rules for Exceptional Groups
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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- | d8c75d9bed6e49a0b8fbcd0350c51ba93f48e9dd
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.
>
> Before the patch, the following rules are not implemented.
>
> {{{
> E6 => C4 , A2 , G2 , A2xG2
> E7 => A2 , A1 , A1 , A1xF4 , G2xC3 , A1xG2 , A1xA1
> E8 => G2xF4 , C2 , A1xA2 , A1 , A1 , A1
> F4 => A1 , A1xG2
> G2 => A1
> }}}
>
> Many of these are implemented in the patch. The patch implements
> {{{
> E6 => C4, A2, G2, A2xG2
> E7 => A1 , A1 , A1xF4 , G2xC3
> E8 => G2xF4 , A1 , A1 , A1
> F4 => A1 , A1xG2
> G2 => A1
> }}}
>
> 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 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")}}}
> The thematic tutorial is revised.
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.
{{{
E6 => C4 , A2 , G2 , A2xG2
E7 => A2 , A1 , A1 , A1xF4 , G2xC3 , A1xG2 , A1xA1
E8 => G2xF4 , C2 , A1xA2 , A1 , A1 , A1
F4 => A1 , A1xG2
G2 => A1
}}}
All but five of these are implemented in the patch. The patch implements
{{{
E6 => C4, A2, G2, A2xG2
E7 => A1 , A1 , A1xF4 , G2xC3
E8 => G2xF4 , A1 , A1 , A1
F4 => A1 , A1xG2
G2 => A1
}}}
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 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")}}}
The thematic tutorial is revised.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/15361#comment:41>
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