On 11/10/14 2:47 PM, Andrew wrote:
>
>
> On Tuesday, 11 November 2014 01:08:08 UTC+11, Nicolas M. Thiery wrote:
>
> On Thu, Nov 06, 2014 at 04:51:40PM -0800, Anne Schilling wrote:
> > Wouldn't it make most sense to use the quadratic relation
> >
> > $(T_r-q)(T_r-v)=0$
> >
> > since the other ones can be obtained by appropriate specialization?
>
> I definitely vote for this as well.
>
>
> This is probably the most sensible thing to do, and certainly seems to be the
> consensus. Just for fun there are also "degenerate" and "non-degenerate"
> forms of these representations.
>
> I'm slightly bemused, however, because I'm fairly sure that, for the
> quadratic relation (T_r-u)(T_r-v), these representations do not exist in the
> literature. Consequently, I suspect that this level
> of generality will never be used. There may also be a speed penalty because
> rational function fields in one variable are probably more efficient than
> function fields in two variables (for type B and
> higher this comment isn't relevant.). On the other hand, allowing a general
> quadratic relation is probably the easiest way to support the two most common
> forms of the quadratic relations:
> (T_r-q)(T_r+1)=0 and (T_r-q)(T_r+q^{-1})=0. (Btw, the same remarks apply to
> the implementation of the KL-bases in sage: what we have is more general than
> you will find in the literature and it
> automatically works for different quadratic relations and for arbitrary
> coefficient rings provided that the KL-bases are well-defined.)
>
> sage/combinat/root_system/hecke_algebra_representation.py
>
>
> I didn't know about the HeckeAlgebraRepresentation class that is defined in
> this module. I have defined a class, IwahoriHeckeAlgebraRepresentation, that
> is meant to be a generic class for defining
> representations of an Iwahori-Hecke algebra as CombinatorialFreeModules. The
> class in root_system is mainly for affine Hecke algebras and it is quite
> different to what I am doing, but even so I am
> slightly uneasy about introducing a new class that has a similar name and
> functionality to an existing class. It seems to me that a better name for the
> root_system class is
> *Affine*HeckeAlgebraRepresentation, at least this would help distinguish
> between the two. Perhaps this code would also sit more naturally in the new
> directory sage.algebras.iwahori_hecke_algebras? Is
> there a better name for my class? Does anyone have any thoughts on this?
> (Particularly Anne and Nicolas as this is their code...)
We needed the code in sage/combinat/root_system/hecke_algebra_representation.py
to compute the nonsymmetric
Macdonald polynomials. I am ok with renaming it
AffineHeckeAlgebraRepresentation if it does not
break too much backward compatibility. On the other hand, you are naming your
class
IwahoriHeckeAlgebraRepresentation, so perhaps that is good enough!?
Anne
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