#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?, Dan
Authors: Brant Jones, | Bump?
Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: #13735 #14014 |
#14678 #14516 |
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Comment (by andrew.mathas):
Replying to [comment:20 tscrim]:
> Hey Darij,
>
> Thanks for looking over the documentation. As for the `q`, in order to
do what you're suggesting means we have to do all computations in a formal
variable and then specialize. However I don't think this is the correct
behavior, especially when `q` is a root of unity, but I don't know if the
bar involution is still useful at specialized `q`. The problem in my mind
is take `q = 2` and consider the element `2`, what is the bar of this,
does it matter if it's `1 + 1` or `2 in ZZ` or suppose to be the `q`?
>
> Andrew, Dan, Brant, or someone who understands Hecke algebras better
than myself, do you have any thoughts on this? Also would any of you have
time to do the last (math) review of this patch?
>
> Best,[[BR]]
> Travis
The correct way of doing this is to work with an indeterminant/formal
variable to compute the KL-basis elements and then specialise. The bar
involution really only makes sense when q is generic.
Andrew
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Ticket URL: <http://trac.sagemath.org/ticket/14261#comment:24>
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