Hi Anne,
I think that putting in the extra parameter for the
type of core is a good idea. No parameter is all
cores (type A).
The type C is symmetric cores (from your paper)
and type B is symmetric even cores (and I forget
what type D is)?
I think that affine Grassmannian to core and partition should
go in Weyl groups.
The type C partitions in Brant and Chris H.'s paper
say (if I remember correctly) that type C partitions are
strict in 1,2,...,n and 2n bounded
and type B partitions are strict in 1,2,...,n-1, and 2n-1 bounded.
-Mike
On Fri, Aug 26, 2011 at 10:28 AM, Anne Schilling <a...@math.ucdavis.edu> wrote:
> Hi Mike,
>
> Great! I suppose in type C you would go to symmetric cores
> (as in my paper with Thomas and Mark). Where should the
> inverse function go, that is, the function from symmetric
> cores to affine Grassmannian elements in type C? Also in the
> Core class? But then the function would have to take another
> argument, namely the type and do some checking (that the core is
> symmetric etc).
>
> We can ask Brant and Steve! I agree they are not difficult
> to implement, I am just wondering where precisely to put them
> in sage.
>
> Best,
>
> Anne
>
>
> On 8/26/11 7:16 AM, Mike Zabrocki wrote:
>>
>> Hi Anne,
>> I have these functions in type C and I
>> can do type B and D too (I just have been
>> waiting on my student to do them). I haven't
>> looked too closely, but I think that they can
>> be done in a way that tweaks just one line.
>>
>> Maybe Brant has already done them?
>>
>> -Mike
>>
>> On Fri, Aug 26, 2011 at 2:12 AM, Anne Schilling<a...@math.ucdavis.edu>
>> wrote:
>>>
>>> Hi!
>>>
>>> A first implementation of the Core class is now available in the patch
>>>
>>> trac_11742-cores-as.patch
>>>
>>> on the sage-combinat server. Any comments or volunteers for review?
>>> (Could Mike and I be both authors and reviewers at the same time?)
>>>
>>> I have a question regarding one more detail: We implemented the bijection
>>> between k-bounded partitions and (k+1)-cores as the methods
>>> to_core in Partition and to_bounded_partition in Core.
>>> There is also a bijection with Grassmannian elements in the affine Weyl
>>> group
>>> for type A_k^{(1)}. There are methods from_kbounded_to_grassmannian in
>>> Partition
>>> and to_grassmannian in Core.
>>>
>>> Where shall we put the corresponding reverse maps from Grassmannian
>>> elements?
>>> Should they go into /combinat/root_system/weyl_group.py?
>>> This is, however, currently specific to type A and Grassmannian elements.
>>>
>>> Cheers,
>>>
>>> Anne
>
>
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