Hi Benjamin,
This is very nice! Thanks for implementing it. One question I have is
how easy it would be to upgrade this to also compute affine Demazure
characters. I suppose WeylCharacterRing does not yet exist in this
setting, right?
Best wishes,
Anne
On 2/4/11 1:30 PM, BFJ wrote:
Hi all,
This is now Trac #10744 (http://trac.sagemath.org/sage_trac/ticket/
10744). I've uploaded a patch to provide demazure_character (based on
Daniel Bump's patch above), plot, and degree for the WeightRingElement
class.
Comments, suggestions, and kibitzing are appreciated!
--
Benjamin Jones
University of Wisconsin-Stout
[email protected]
[email protected]
On Feb 1, 1:54 pm, BFJ<[email protected]> wrote:
Ok, great. I'll start working on a patch and reply here again when
it's on the trac server.
--
Benjamin Jones
University of Wisconsin-Stout
[email protected]
[email protected]
On Jan 31, 2:17 pm, Daniel Bump<[email protected]> wrote:
I don't know if it's helpful to post so much code, but here is my code
for the Demazure character and rank 2 plotting. The Demazure character
code contains the same idea as bump's code.
There were a couple of mistakes in the code snippet that I posted.
Here is another attempt, probably correct:
http://match.stanford.edu/bump/patches/demazure.patch
After this patch you can do this:
sage: B2 = WeylCharacterRing("B2")
sage: b2 = WeightRing(B2)
sage: W = B2.space().weyl_group(prefix="s")
sage: [s1,s2] = W. simple_reflections()
sage: w0 = W.long_element()
sage: [b2(h).demazure(w0) for h in B2.space().fundamental_weights()]
[b2(-1,0) + b2(0,-1) + b2(0,0) + b2(0,1) + b2(1,0), b2(-1/2,-1/2) +
b2(-1/2,1/2) + b2(1/2,-1/2) + b2(1/2,1/2)]
sage: [b2(B2(h)) == b2(h).demazure(w0) for h in
B2.space().fundamental_weights()]
[True, True]
I should add more examples and flesh out the docstrings, of course. I
need to clean up my plotting code a bit as well.
I'd be happy to start a ticket to add the following methods to
WeightRingElement:
Sure, go ahead and make a ticket. If you want to work on a patch, I can kibbitz.
I won't work on this any more if you want to do it. (I need Demazure
characters for my own work.)
As for waiting for #7922, my belief is that the amount of code that we are
talking about is not so great that we cannot reimplement quickly. So we
should not wait.
Dan
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