Dear all,
here is some question on branching rules that I have little clue about.
Best,
Dima
---------- Forwarded message ----------
From: Daniel Miller (dmillera) <dmill...@micron.com>
Date: 5 October 2013 19:38
Subject: Left-Right asymmetry in D8->D2xD2 and other "tensor" branching rules
To: "Dmitrii V Pasechnik (Dr)" <d...@ntu.edu.sg>
Dear Dmitrii,
Thank you for mentioning me SAGE,
I've really enjoyed running it, particularly on cloud server.
By the way,
I've noticed strange asymmetry for branching of left/right spinor
representations, see below.
SO(12)->SO(3) x SO(4), "tensor" - ok
SO(16)->SO(4) x SO(4), "tensor" - asymmetric
SO(24)->SO(6) x SO(4), "tensor" - asymmetric
Please let me know if this is known issue, or I do something obviously wrong.
Please ignore, if you are busy.
Regards Daniel.
## Good Example
## SO(12) -> SO(3) x SO(4)
D6 = WeylCharacterRing("D6", style="coroots")
B1xD2 = WeylCharacterRing("B1xD2", style="coroots")
adjnt = D6(D6.fundamental_weights()[2]); adjnt
spinL = D6(D6.fundamental_weights()[5]); spinL
spinR = D6(D6.fundamental_weights()[6]); spinR
adjnt.branch(B1xD2, rule="tensor"),spinL.branch(B1xD2,
rule="tensor"),spinR.branch(B1xD2, rule="tensor")
#
#(B1xD2(2,0,0) + B1xD2(2,2,2) + B1xD2(4,2,0) + B1xD2(4,0,2) +
B1xD2(0,2,0) + B1xD2(0,0,2),
# B1xD2(2,1,2) + B1xD2(4,1,0) + B1xD2(0,3,0),
# B1xD2(2,2,1) + B1xD2(4,0,1) + B1xD2(0,0,3))
#
# 66 -> 3 * 1 + 3 * 9 + 5 * 3 + 5 * 3 + 1 * 3 + 1 * 3
# 32 -> 18 + 10 + 4 = 3*6 + 5 * 2 + 1 * 4
# 32 -> 18 + 10 + 4 = 3*6 + 5 * 2 + 1 * 4
## Strange example
##
## SO(16) decomposition to product SO(4) X SO(4)
##
D8 = WeylCharacterRing("D8", style="coroots")
D2xD2 = WeylCharacterRing("D2xD2", style="coroots")
#
adjnt = D8(D8.fundamental_weights()[2]); adjnt
spinL = D8(D8.fundamental_weights()[7]); spinL
spinR = D8(D8.fundamental_weights()[8]); spinR
adjnt.branch(D6xD2, rule="extended")
# D6xD2(0,1,0,0,0,0,0,0) + D6xD2(1,0,0,0,0,0,1,1) +
D6xD2(0,0,0,0,0,0,2,0) + D6xD2(0,0,0,0,0,0,0,2),
# 120 -> 66*1 + 12 * 4 + 1 * 3 + 1 * 3
#
# I cannot understand the left-right symmetry breaking here:
spinL.branch(D2xD2, rule="tensor")
# D2xD2(1,1,3,1) + D2xD2(1,1,1,3) + D2xD2(3,1,1,1) + D2xD2(1,3,1,1),
#
spinR.branch(D2xD2, rule="tensor")
# D2xD2(2,0,2,2) + D2xD2(0,2,2,2) + D2xD2(4,0,0,0) + D2xD2(0,4,0,0)
# + D2xD2(2,2,2,0) + D2xD2(2,2,0,2) + D2xD2(0,0,4,0) + D2xD2(0,0,0,4)
#
# What the hell???
# 128 -> 4 * 8 + 4 * 8 + 8 * 4 + 8 * 4
# 128 -> 3 * 9 + 3 * 9 + 5*1 + 5 * 1 + 9 * 3 + 9 *3 + 1 * 5 + 1 * 5
-----Original Message-----
From: Dmitrii (Dima) Pasechnik [mailto:d...@ntu.edu.sg]
Sent: Thursday, August 22, 2013 8:34 AM
To: Daniel Miller (dmillera)
Cc: supp...@gap-system.org
Subject: Re: [GAP Support] Lie Algebra D(N) branching rules with GAP4
On 15 August 2013 16:54, Daniel Miller (dmillera) <dmill...@micron.com> wrote:
> Hello folks,
> I've wrote nice GAP4 script calculating D(N) = SO(2N) branching rules.
> It is not speed optimized, may be someone in the community can do it better
> / faster.
>
> Probably this is something well-known before, I was not able to find any
> relevant software.
> I don't know if Mathematica / Mathcad / Matlab have this feature.
Sage can do quite a few branching rules, see e.g.
http://www.sagemath.org/doc/thematic_tutorials/lie/branching_rules.html
Just in case,
Dmitrii
> Daniel.
>
> http://criblycrablybum.livejournal.com/289182.html
> _______________________________________________
> Support mailing list
> supp...@mail.gap-system.org
> http://mail.gap-system.org/mailman/listinfo/support
CONFIDENTIALITY:This email is intended solely for the person(s) named
and may be confidential and/or privileged.If you are not the intended
recipient,please delete it,notify us and do not copy,use,or disclose
its content.
Towards A Sustainable Earth:Print Only When Necessary.Thank you.
--
You received this message because you are subscribed to the Google Groups
"sage-combinat-devel" group.
To unsubscribe from this group and stop receiving emails from it, send an email
to sage-combinat-devel+unsubscr...@googlegroups.com.
To post to this group, send email to sage-combinat-devel@googlegroups.com.
Visit this group at http://groups.google.com/group/sage-combinat-devel.
For more options, visit https://groups.google.com/groups/opt_out.
