#20469: Implement Ariki-Koike algebras
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.3
Component: algebra | Resolution:
Keywords: hecke algebra, | Merged in:
complex reflection group, ariki- |
koike |
Authors: Travis Scrimshaw, | Reviewers: Andrew Mathas, Travis
Andrew Mathas | Scrimshaw
Report Upstream: N/A | Work issues:
Branch: | Commit:
public/algebras/ariki_koike_algebras-20469|
e9b6a594ae1e089b51b37081f35743402447a960
Dependencies: | Stopgaps:
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Comment (by tscrim):
Replying to [comment:11 andrew.mathas]:
> Replying to [comment:10 tscrim]:
> > Replying to [comment:8 andrew.mathas]:
>
> > I'm +1 for getting things closer to the KLR algebra (something that I
hope to eventually get into Sage at some point). Otherwise I don't have an
opinion on which presentation we use. How much would have to be changed in
order to move to the Hu-Mathas presentation?
>
> With all of these things it is mainly a matter of implementing
appropriate analogues of the three methods `_product_LTwTv`,
`_product_Tw_L`, and `_Li_power` that underpin the multiplication.
Replacing `q` with a two variable version may be the hardest option as
we'd have to think what the appropriate normalisation of the Jucys-Murphy
elements is. This said, I would prefer to have the more symmetric
relations `(T_i-q)(T_i+q^{-1})=0`, so I will have a think about this.
I believe I've said this above, but to be pedantic, I have no preference
as to what quadratic relation is. How much could be obtained by looking at
the affine Hecke algebra and passing to the quotient?
> Regarding KLR algebras, implementing the "affine" KLR algebras is
reasonably straightforward. I know now of a way to do the cyclotomic
quotients in a few cases and I will implement them at some point, although
the isomorphism to the ungraded algebras is much harder to do.
Please cc me on that ticket when you create it. I would be happy to review
it.
--
Ticket URL: <https://trac.sagemath.org/ticket/20469#comment:12>
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