#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, 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 nthiery):
Replying to [comment:46 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,
> }}}
> as we currently have it, or should they be
> {{{
> (T_r-q1)(T_r+q2)=0?
> }}}
> There are advantages and disadvantages with both choices. I don't really
care either way, but I thought that the question 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 arguably 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).
Unsurprisingly, choice 1 is my preferred. It makes their description easy
and symmetric: the two eigenvalues of the T's.
Thanks!
--
Ticket URL: <http://trac.sagemath.org/ticket/14261#comment:47>
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