#14261: Iwahori-Hecke algebra with several bases
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Reporter: brant | Owner: sage-combinat
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-5.12
Component: combinatorics | Resolution:
Keywords: Iwahori Hecke | Merged in:
algebra | Reviewers: Andrew Mathas, Brant
Authors: Brant Jones, | Jones, Travis Scrimshaw
Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: #13735 #14014 |
#14678 #14516 |
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Comment (by nthiery):
Replying to [comment:40 andrew.mathas]:
> Unfortunatey, having user supplied bar involution isn't going to
> work here. For example, it makes perfect sense to talk about the
> Kazhdan-Lusztig bases of the group ring `ZW` (by specialisation) BUT
> you can can't define an appropriate bar involution on `ZW`. The
> point is that you can't detect the KL-bases inside `ZW`: to find
> them you have to work generically and then specialise -- that is,
> you have to work in a completely different (but related) algebra to
> define these bases.
Yes, that's what I meant above by "when it makes sense". When it does
not you certainly have to go through generic/specialization.
My point is that, when it makes sense, it could be worthwhile making
explicit (and customizable!) what the involution on the ground field
does. In particular for potential use cases where the bar involution
on the ground field is non trivial. In which case the user could
provide an implementation of it to bypass the generic/specialization
process.
Cheers,
Nicolas
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Ticket URL: <http://trac.sagemath.org/ticket/14261#comment:44>
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