Branching rule A2->A1 never returns

[vbraun]

The following goes into an infinite loop and never returns:

sage: A2 = WeylCharacterRing('A2', style='coroots')
sage: A1 = WeylCharacterRing('A1', style='coroots')
sage: A2(1,0).branch(A1)

---

Apply:

• attachment: trac_15023_branch.patch​
• attachment: trac_15023-review-ts.patch

CC: @sagetrac-sage-combinat @dwbump

Component: combinatorics

Keywords: "branching rule"

Author: Daniel Bump

Reviewer: Travis Scrimshaw

Merged: sage-5.12.beta3

Issue created by migration from https://trac.sagemath.org/ticket/15023

[dwbump]

comment:1

This works:

sage: A2(1,0).branch(A1,rule="levi")
A1(0) + A1(1)

But it remains a problem that the code is not very forgiving if you forget to specify a branching rule. There are two possible approaches to fixing this.

The first would be to raise a ValueError if the branching rule is omitted. The second would be to try to guess the branching rule by consulting a table. The first way would be easy to implement and I can submit a patch for it.

[vbraun]

comment:2

Though generally the default rule works, its just here that it doesn't. It is a convenient feature to let Sage guess the branching rule, so having some heuristic / a table would be nice.

If you really don't want to have a default then rule shouldn't be a optional keyword argument: def branch(weyl_character_ring, rule): would always force the user to enter something.

[dwbump]

comment:3

Though generally the default rule works, its just here that it doesn't. It is a
convenient feature to let Sage guess the branching rule, so having some heuristic / a table would be > nice.

I agree and I am thinking the default branching rule should be to do the obvious thing
in the following cases:

(1) Top Cartan type is irreducible and restriction is to a Levi.
(2) The top group is type A_r, and the bottom group is embedded
    by means of its standard representation. This includes three
    cases B_r -> A_{2r}, C_r -> A_{2r-1} and D_r -> A_{2r-1}.
    Equivalently, either O(n) -> SL(n) or Sp(2n) -> SL(2n).
(3) O(n) -> O(n-1).

That might be enough for an initial implementation. I thought of adding Sp(2n)->Sp(2n-2) to this list but this BR factors through Sp(2n-2)xA1 which is a Levi branching.

These are the default rules implemented by the patch. If a default rule is not found, an error is raised.

[dwbump]

Attachment: trac_15023_branch.patch.gz

#15023: implements correct default branching rules

[dwbump]

Author: bump

[dwbump]

Changed keywords from none to "branching rule"

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

Changed author from bump to Dan Bump

[tscrim]

comment:8

Hey Dan,

Here's a review patch which removes the bare except: statements, does some doc formatting (in preparation of #15042), and re-organizes the code to make it easier to read (to me at least). If you're happy with my changes, you can go ahead and set this to positive review.

[dwbump]

comment:9

Thanks Travis. The reviewer patch looks good. I'll wait until tomorrow or so to set pos review since Volker Braun might have some comment.

[vbraun]

comment:10

Looks good to me, thanks!

[tscrim]

comment:11

Your welcome. Thanks.

[tscrim]

comment:12

Attachment: trac_15023-review-ts.patch.gz

I had to do a minor tweak to catch an A₁ issue (change an elif to an if).

[jdemeyer]

Merged: sage-5.12.beta3

[fchapoton]

Changed author from Dan Bump to Daniel Bump