#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 darij):
I've just looked into the patch to see how algebras with multiple bases
are implemented; I don't really know (or care much, by now) about Hecke
algebras. I've uploaded a few superficial docstring fixes.
An issue I'm not fixing but you might want to ponder about are the
docstrings of {{{bar(self)}}} and {{{hecke_involution(self)}}}. They
pretend that these methods send the deformation variable {{{q}}} to
{{{q^(-1)}}} (or {{{q^(1/2)}}} to {{{q^(-1/2)}}}, which is more or less
the same). But what they actually invert is not the deformation variable,
but rather the indeterminates generating the Laurent polynomial ring in
which the deformation variable resides. So if the deformation variable is,
say, {{{2t}}}, then {{{t}}} is sent to {{{t^(-1)}}}, not {{{2t}}} to
{{{(2t)^(-1)}}}. I don't know in how far this issue will pop up in real
life, but here's an example:
{{{
sage: W.<t> = LaurentPolynomialRing(QQ)
sage: H = IwahoriHeckeAlgebra(['A',3], 2*t)
sage: T = H.T()
sage: T1,T2,T3 = T.algebra_generators()
sage: T1.bar()
(1/2*t^-1)*T1 + (-1+1/2*t^-1)
sage: (t*T1).bar()
(1/2*t^-2)*T1 + (-t^-1+1/2*t^-2)
}}}
--
Ticket URL: <http://trac.sagemath.org/ticket/14261#comment:19>
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