#15361: Branching Rules for Exceptional Groups
-------------------------------------+-------------------------------------
Reporter: bump | Owner: bump
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- | faec22739d4590ddc1cc5d72490f5381fbb908fd
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
> }}}
>
> With the patch, ALL of these are now implemented in Sage. After the
> patch, every
> branching rule in the tables of McKay and Patera (Tables of dimensions,
> indices and branching rules for representations of simple Lie algebras)
> is available in Sage!
>
> Here is a file that constructs the branching rule for every maximal
> subgroup of every simple Lie group of rank less than or equal to 8. This
> includes every case considered by McKay and Patera, and every exceptional
> group.
>
> http://sporadic.stanford.edu/bump/branch-table.sage
>
> The embeddings are described in the thematic tutorial. I've posted a copy
> of the patched tutorial and reference manual on sporadic.stanford.edu.
> The relevant sections are here:
>
> http://sporadic.stanford.edu/thematic_tutorials/lie/branching_rules.html
> http://sporadic.stanford.edu/reference/combinat/sage/combinat/root_system/weyl_characters.html
> http://sporadic.stanford.edu/reference/combinat/sage/combinat/root_system/branching_rules.html
>
> 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. The thematic
> tutorial is revised.
>
> Since weyl_characters.py was getting huge, I split it, moving the
> branching rule material into a new file, branching_rules.py.
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
}}}
With the patch, ALL of these are now implemented in Sage. After the patch,
every
branching rule in the tables of McKay and Patera (Tables of dimensions,
indices and branching rules for representations of simple Lie algebras) is
available in Sage!
Here is a file that constructs the branching rule for every maximal
subgroup of every simple Lie group of rank less than or equal to 8. This
includes every case considered by McKay and Patera, and every exceptional
group.
http://sporadic.stanford.edu/bump/branch-table.sage
The embeddings are described in the thematic tutorial. I've posted a copy
of the patched tutorial and reference manual on sporadic.stanford.edu. The
relevant sections are here:
http://sporadic.stanford.edu/thematic_tutorials/lie/branching_rules.html
http://sporadic.stanford.edu/reference/combinat/sage/combinat/root_system/weyl_characters.html
http://sporadic.stanford.edu/reference/combinat/sage/combinat/root_system/branching_rules.html
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. The thematic tutorial is
revised.
Since weyl_characters.py was getting huge, I split it, moving the
branching rule material into a new file, branching_rules.py.
--
--
Ticket URL: <http://trac.sagemath.org/ticket/15361#comment:58>
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