#20469: Implement Ariki-Koike algebras
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Reporter: tscrim | Owner: sage-combinat
Type: enhancement | Status: new
Priority: major | Milestone: sage-7.2
Component: algebra | Resolution:
Keywords: hecke algebra, | Merged in:
complex reflection group, ariki- | Reviewers:
koike | Work issues:
Authors: Travis Scrimshaw | Commit:
Report Upstream: N/A | f644c20f0c297faf9dc98e4bab70c5985131d390
Branch: | Stopgaps:
public/algebras/ariki_koike_algebras-20469|
Dependencies: |
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Comment (by andrew.mathas):
Thanks Travis. This looks interesting. I will have a play with it and see
if I can improve the multiplication with the tricks that I know about
these algebras -- I am not promising that this will be possible, only to
look!
Some initial comments:
- It would be better to use `L1`,...,`Ln` for the Jucys-Murphy elements as
this is what is commonly used in the literature and it's also consistent
with using `T1`,`T2`,... for the Hecke generators.
- I am not sure that it is worth the effort to define the Hu-Mathas as the
algebras that we defined are different to these when `q=1` and, more
importantly, the conversion between the two is easy in principle but messy
in practice.
- The default base ring should be the smallest ring that contains `q`,
`u0`,...,`ur`.
- At some stage I will polish the code that I have which implements the
Specht modules for these algebras. Given this it would probably be a good
idea to put this code in its own subdirectory so that the module code.
Similarly, my graded Specht module could go in here to.
--
Ticket URL: <http://trac.sagemath.org/ticket/20469#comment:3>
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