#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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Changes (by tscrim):
* cc: andrew.mathas (added)
* commit: => f644c20f0c297faf9dc98e4bab70c5985131d390
* branch: => public/algebras/ariki_koike_algebras-20469
Comment:
Here is the first version. I still have to convert from Ariki-Koike's
version to the Hu-Mathas definition, but this version seems to work (in
particular, it passed a few of my associativity tests and the relations I
tested). There is also more documentation that needs to be added. I'm also
not completely satisfied with the default base ring. However, I wanted to
get feedback.
Note that the multiplication is highly recursive. In particular, once
there is an l,,i,,^r occurring, it can easily run into Python's recursion
limit. It might be possible to work this out with handling the
manipulations within the code here or doing parts of the multiplication in
bigger chunks. However, this would take a lot of work I think to improve
and the code works.
I am also planning on implementing the isomorphism with type A,,n,,/B,,n,,
Hecke algebras shortly too.
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New commits:
||[http://git.sagemath.org/sage.git/commit/?id=f644c20f0c297faf9dc98e4bab70c5985131d390
f644c20]||{{{Initial implementation of Ariki-Koike alegbras.}}}||
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Ticket URL: <http://trac.sagemath.org/ticket/20469#comment:2>
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