#14261: Iwahori-Hecke algebra with several bases
-------------------------------------+-------------------------------------
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, Brant
Authors: Brant Jones, | Jones, Travis Scrimshaw
Travis Scrimshaw | Work issues:
Report Upstream: N/A | Commit:
Branch: | Stopgaps:
Dependencies: #13735 #14014 |
#14678 #14516 |
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Comment (by andrew.mathas):
'''Default parameters for the Hecke algebras'''
We are implementing Hecke algebras with two parameters `q1` and `q2`.
Should the corresponding quadratic relations be
{{{
(T_r-q1)(T_r-q2)=0,
}}}
, and we currently have it, or should they be
{{{
(T_r-q1)(T_r+q2)=0?
}}}
There are advantages and disadvantes with both choices. I don't really
care either way, but I thought that the questions should be at least asked
because the three "most common" choices for relations are:
{{{
(T_r-q)(T_r+1)=0 # Iwahori's original defintiion
(T_r-q)(T_r+q^-1)=0 # the best normalistion
(T_r-1)(T_r+1)=0 # the group ring of the Coxeter group
}}}
All of these are arugably more compatible with the second choice.
If no one has a strong preference either way then I will leave it as it is
(choice 1).
--
Ticket URL: <http://trac.sagemath.org/ticket/14261#comment:46>
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