#17989: Double Affine Hecke Algebra
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Reporter: nthiery | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.6
Component: combinatorics | Resolution:
Keywords: daha, days64 | Merged in:
Authors: Mark Shimozono | Reviewers: Dan Bump, ...
Report Upstream: N/A | Work issues:
Branch: | Commit:
u/mshimo/combinat/double_affine_hecke_algebra|
da9705f7d218478f6d5e24adce0872b4196198ba
Dependencies: | Stopgaps:
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Comment (by nthiery):
Some notes from the discussion at SD64:
* Generic features to be extracted from #15375
- Exp functor:
Currently in sage/groups/exp.py ; could be sage/monoids/exp.py
class Exp(...)
def log(self):
return self._log
sage: Exp(my_additive_group)
sage: Exp(additive_group_morphism)
sage: my_additive_group.exp() # return the associated
multiplicative group
Possibly make it a functorial construction (can be postponed to later):
Create sage.categories.additive_group_exp along the lines of
sage.categories.cartesian_product
class AdditiveMagmas:
class Exp:
class ParentMethods:
@abstract_method
def log(self):
...
class ElementMethods:
def _mul_(self, other):
return self.parent()(self.value+other.value)
class Unital:
class Exp:
class ParentMethods:
def one():
return self(self.log().zero())
....
- Semidirect product of groups:
Put Mark's implementation in
sage.groups.semidirect_product.SemiDirectProduct
Have Groups.ParentMethods.semidirect_product call it (currently it
says NotImplemented)
Bonus: if PermutationGroup.semidirect_product is called with the
second group not being a permutation group, call the generic
implementation. Same for finitely presented groups.
* Generic features to be extracted from #17989 (Daha)
- Improvements to tensor products
- Tensor product of morphisms (see ticket by Nicolas Borie?)
- Tensor products without flattening? For tensor product of algebras
What happens in Sage if you one does a tensor product of algebras
that are themselves tensor products? *boom*
To be further discussed; probably tensor_product should take a flag
flatten=True
- Smash product
--
Ticket URL: <http://trac.sagemath.org/ticket/17989#comment:2>
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