#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):
Given the issues that we're having in computing the KL bases I think that
we need some basic tests like:
{{{
sage: T(Cp(1))
v^-1*Cp1 + v^-1
sage: T(C(1))
v^-1*Cp1 - v
sage: C(Cp(1))
C1 + (v+v^-1)
sage: Cp(C(1))
Cp1 + (-v-v^-1)
}}}
I think that there also should be long tests like:
{{{
sage: forall( C(x)==C(T(x)) for x in W )
true
sage: forall( C(x)==C(Cp(x)) for x in W )
true
sage: forall( Cp(x)==Cp(T(x)) for x in W )
true
sage: forall( Cp(x)==Cp(C(x)) for x in W )
true
}}}
where W is at least Sym(4) or of type B2 or ...
As there is an independent implementation of the KL-polys inside sage (I
think???) it should also be possible to do something like:
{{{
sage: T(Cp(x)) == v^-x.length()*sum( KLPoly(y,x)*T(y) for y in W)
}}}
Apologies but I don't know the right syntax here.
--
Ticket URL: <http://trac.sagemath.org/ticket/14261#comment:23>
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