#7729: Iwahori Hecke algebras [with patch, needs review]
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Reporter: bump | Owner: bump
Type: enhancement | Status: needs_review
Priority: major | Milestone: sage-4.3.1
Component: combinatorics | Keywords: Iwahori Hecke Algebra
Work_issues: | Author: Daniel Bump
Upstream: N/A | Reviewer:
Merged: |
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Description changed by bump:
Old description:
> The attached patch implements Iwahori Hecke algebras. Given a Cartan
> Type, the Iwahori Hecke algebra is a deformation of the group algebra
> over the Weyl group. It has generators in bijection with the simple
> reflections of the Weyl group that satisfy simple quadratic relations of
> the form {{{(T_i-q1)*(T_i-q2)}}} = 0. Often we default q2=-1, q1=q in
> which case the relation is of the form {{{T_i^2=(q-1)T_i+q}}}. The
> generators also satisfy the braid relations.
>
> {{{
> sage: R.<q>=PolynomialRing(QQ)
> sage: H = IwahoriHeckeAlgebra("A3",q)
> sage: [T1,T2,T3]=H.algebra_generators()
> sage: T1*(T2+T3)*T1
> T1*T2*T1 + (q-1)*T3*T1 + q*T3
> }}}
>
> For some further discussion of this topic see
> http://groups.google.com/group/sage-combinat-
> devel/browse_thread/thread/78fc23f23cafe705?hl=en
New description:
The attached patch implements Iwahori Hecke algebras. Given a Cartan Type
(finite or affine), the Iwahori Hecke algebra is a deformation of the
group algebra over the Weyl group. It has generators in bijection with the
simple reflections of the Weyl group that satisfy simple quadratic
relations of the form {{{(T_i-q1)*(T_i-q2)}}} = 0. Often we default q2=-1,
q1=q in which case the relation is of the form {{{T_i^2=(q-1)T_i+q}}}. The
generators also satisfy the braid relations.
{{{
sage: R.<q>=PolynomialRing(QQ)
sage: H = IwahoriHeckeAlgebra("A3",q)
sage: [T1,T2,T3]=H.algebra_generators()
sage: T1*(T2+T3)*T1
T1*T2*T1 + (q-1)*T3*T1 + q*T3
}}}
For some further discussion of this topic see
http://groups.google.com/group/sage-combinat-
devel/browse_thread/thread/78fc23f23cafe705?hl=en
--
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/7729#comment:11>
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