#15508: Implement Fock space
-------------------------------------+-------------------------------------
Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-6.0
Component: algebra | Resolution:
Keywords: Fock space | Merged in:
quantum group representations | Reviewers:
Authors: Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | 4548a5b5788962a11afdb40c2786d816cda07183
public/modules/fock_space | Stopgaps:
Dependencies: #15289 |
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Comment (by tscrim):
Hey Andrew,
Replying to [comment:2 andrew.mathas]:
> Thanks for both working on this and for letting me know about it. I just
had a quick glance through it and it looks very nice, but there is a lot
of code to digest! The fact that the new improved git-world makes it
difficult to separate the current ticket from its dependencies makes this
harder of course.
Actually, there's not a functional dependency on #15289, just some syntax,
so I can commute this past with relative ease if #15289 doesn't get
reviewed before we are done with this.
> I will try and look through this properly in due course as it is one of
the things that I care about - and implementing this was on my to-do list.
>
> A few questions/comments (based on my very quick read through):
>
> * [I]n his paper Fayers' has a conjecture for the degrees of the
polynomials that came up (they should always be less than the
defect/weight), ... Fayers' conjecture is now known to be true, so I was
wondering whether you have used this in your code.
No I do not. Currently I don't check if a partition is regular, so I guess
I'm really computing for the full tensor product space. I should also note
another abuse; my indexing set for the highest weight modules is too large
(I'm using all partitions instead of just the `n`-regular and giving an
error when the user tries to create a non-`n`-regular partition). I
probably should change that... [[BR]] `>.>` [[BR]] `<.<`
> * Am I right in thinking that you have only implemented the Fock spaces
`F(\Lambda)` such that `F(\Lambda)\cong
F(\Lambda_{a_1})\otimes\dots\otimes F(\Lambda_{a_k})`, for dominant
weights `\Lambda=\Lambda_{a_1}+\dots+\Lambda_{a_k}`?
Correct.
> In addition to these "standard" Fock spaces there are some more
general Fock spaces for `U_q(\widehat{sl}_e)` defined by Uglov. I am
asking this more for information/clarification as Uglov's Fock spaces
don't come up in my work - they arise in the cateogorification of rational
Cherednik algebras.
Hmm...interesting. Do you have a reference I could look at?
> * In terms of displaying ... I would prefer something like
> {{{
> |3, 1> + q*|2, 2> + q^ 2*|2, 1, 1>
> }}}
> and something similar for higher levels.
I will make this change along with restricting the indexing set to the
proper set.
Best,[[BR]]
Travis
--
Ticket URL: <http://trac.sagemath.org/ticket/15508#comment:3>
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