Opened 6 years ago

# Double Affine Hecke Algebra

Reported by: Owned by: nthiery major sage-8.2 combinatorics daha, days64 sage-combinat, aschilling, bump Mark Shimozono Dan Bump, Travis Scrimshaw, ... N/A public/combinat/double_affine_hecke_algebra-17989 bbb257dd9e1b85087e885e55d2e71a5957c9fa81 #15375

### Description

This ticket implements the Double Affine Hecke Algebra, with multiple bases, ...

### comment:1 Changed 6 years ago by nthiery

• Branch set to u/mshimo/combinat/double_affine_hecke_algebra

### comment:2 Changed 6 years ago 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: 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 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

### comment:3 Changed 6 years ago by git

• Commit changed from da9705f7d218478f6d5e24adce0872b4196198ba to b0415ee829c9946643093faafe3636e94b4ce888

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

 ​d146bdd `Merge branch 'public/combinat/extended_affine_weyl_groups-15375' of git://trac.sagemath.org/sage into public/combinat/extended_affine_weyl_groups-15375` ​870af04 `15375: small change` ​cb2c7d7 `added generators methods` ​09cea03 `Merge branch 'extendedJune9' into nowdaha` ​c5386af `fixing fundamental group list method` ​9e25def `implemented list method for fundamental group` ​c76530b `Merge branch 'extendedJune9' into nowdaha` ​4438e09 `fixed bugs related to finiteness of fundamental group` ​31c67fd `Merge branch 'extendedJune9' into nowdaha` ​b0415ee `fixed doctests in affine hecke algebra`

### comment:4 Changed 6 years ago by mshimo

This is still messed up, specifically deciding the right category for tensor products. However most doctests pass.

### comment:5 Changed 6 years ago by git

• Commit changed from b0415ee829c9946643093faafe3636e94b4ce888 to 22a623bbaac577ff5623d650e1d0958f320bcc12

Branch pushed to git repo; I updated commit sha1. New commits:

 ​addcb09 `fixed group_generators methods` ​c021d03 `15375: removed from_vector_notation` ​b9152e2 `Merge branch 'public/combinat/extended_affine_weyl_groups-15375' of trac.sagemath.org:sage into extended` ​f36f4aa `made fixes suggested by Nicolas; added __iter__ method to fundamental group` ​22a623b `Merge branch 'extended' into daha`

### comment:6 Changed 6 years ago by git

• Commit changed from 22a623bbaac577ff5623d650e1d0958f320bcc12 to 799d8ddce92e0c745f4d8e64ea38cbca987a1de8

Branch pushed to git repo; I updated commit sha1. New commits:

 ​e7aedfc `fixed __iter__ method` ​93f5adf `removed is_finite method for extended affine Weyl groups and added Finite() and Infinite() information to category` ​1c57d0b `Merge branch 'extended' into daha` ​799d8dd `fixed an_element change in doctest in affine_hecke_algebra`

### comment:7 Changed 6 years ago by tscrim

• Dependencies set to #15375

Mainly to cc myself (and a completely shameless plug for the related #18631).

Also #15375 is a dependency, but are there currently others (in particular, #15874)?

### comment:8 Changed 6 years ago by mshimo

Travis,

I had a patch bomb for the DAHA. At some point I forgot to factor out the smash product.

### comment:9 Changed 6 years ago by mshimo

I suppose I could try to look at the diff and factor out the smash product.

### comment:10 Changed 6 years ago by git

• Commit changed from 799d8ddce92e0c745f4d8e64ea38cbca987a1de8 to 199314a36d2239d8807cff10309e073ec25dc5f9

Branch pushed to git repo; I updated commit sha1. New commits:

 ​fd2aa16 `little changes` ​199314a `Merge branch 'extended' into daha`

### comment:11 Changed 6 years ago by git

• Commit changed from 199314a36d2239d8807cff10309e073ec25dc5f9 to 75a717f88f3c8e355b679fa78711ff7460066182

Branch pushed to git repo; I updated commit sha1. New commits:

 ​154656f `little changes` ​6231957 `Merge branch 'extended' into daha` ​4711edf `small changes` ​fee79e7 `changed fundamental_group an_element() to give a nonidentity element when possible; had to fix the doctests` ​2843110 `Merge branch 'extended' into daha` ​6bbf876 `little fixes to fundamental group` ​cece2fb `little fix to family method of GL fundamental group and added a group_generators method for it` ​75a717f `Merge branch 'extended' into daha`

### comment:12 Changed 6 years ago by tscrim

Isn't all of the code for the smash product on #15874? If so, then we'd only have to merge that in and mark that as a dependency. Or is that not necessary for your DAHA code? If that's the case, then we definitely should factor that out.

### comment:13 Changed 6 years ago by mshimo

I will try. I didn't support that branch and just fixed a DAHA branch. So I will have to do some serious checking of versions.

### comment:14 Changed 6 years ago by git

• Commit changed from 75a717f88f3c8e355b679fa78711ff7460066182 to c7a1be25d25c64af43fd1e989873129bbe5e3d5f

Branch pushed to git repo; I updated commit sha1. New commits:

 ​74c53ba `made an_element cached` ​c7a1be2 `tiny changes`

### comment:15 Changed 6 years ago by git

• Commit changed from c7a1be25d25c64af43fd1e989873129bbe5e3d5f to a565f47cbaf37eb185e19a51972776fcd313765d

Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

 ​20db387 `merged smash_product_algebra.py from daha (more advanced branch)` ​fc1ca97 `merged free_module.py from daha (more advanced branch)` ​e089aeb `little relocate` ​182459a `merged from daha` ​21c444e `merged from daha` ​c769387 `merge from daha` ​8a33fa7 `merged from daha` ​0472e45 `merged from daha` ​b3ab187 `fixed doctests in vector spaces` ​a565f47 `Merge branch 'smash_product' into daha`

### comment:16 Changed 6 years ago by git

• Commit changed from a565f47cbaf37eb185e19a51972776fcd313765d to 4f9a4f0a2ebd5696366bc29ba7245c3ac7ced84d

Branch pushed to git repo; I updated commit sha1. New commits:

 ​c0c7c0f `somehow bugfix of trac 18634 was undone. I redid it.` ​a06f404 `some changes Nicolas suggested` ​79d4fe5 `fixing doc strings and implementing more suggestions from Nicolas` ​ba64e29 `more little fixes` ​c36eb6b `added doctest to magma` ​dde0d4e `fixed magma doctests` ​e094313 `made extended affine weyl group into a lazy import` ​3b8c85f `Merge branch 'fixed_extended' into smash_product` ​4f9a4f0 `Merge branch 'smash_product' into daha`

### comment:17 Changed 6 years ago by git

• Commit changed from 4f9a4f0a2ebd5696366bc29ba7245c3ac7ced84d to d8ebd115ea2e669f1889743feb0ffb8563ee446f

Branch pushed to git repo; I updated commit sha1. New commits:

 ​312879b `Merge branch 'fixed_extended' into smash_product` ​bc7700d `small changes` ​d8ebd11 `Merge branch 'smash_product' into daha`

### comment:18 Changed 6 years ago by git

• Commit changed from d8ebd115ea2e669f1889743feb0ffb8563ee446f to 0a8d98b447a1282b5a0a5075900f5fc8898292b0

Branch pushed to git repo; I updated commit sha1. New commits:

 ​0a8d98b `merged with some changes to fundamental group`

### comment:19 Changed 3 years ago by tscrim

Here is a version rebased on 8.2.beta5. It still has some bitrot on it, so things don't really work, but it is a step in the right direction. Although in hindsight, it probably would have been better to take #15874 and rebase that (and its dependency #15832) and work that in, but I forgotten that #15874 was suppose to be a dependency. I have now marked it as such.

Last edited 3 years ago by tscrim (previous) (diff)

### comment:20 Changed 3 years ago by tscrim

• Branch changed from u/mshimo/combinat/double_affine_hecke_algebra to public/combinat/double_affine_hecke_algebra-17989
• Commit changed from 0a8d98b447a1282b5a0a5075900f5fc8898292b0 to bbb257dd9e1b85087e885e55d2e71a5957c9fa81
• Milestone changed from sage-6.6 to sage-8.2
• Reviewers changed from Dan Bump, ... to Dan Bump, Travis Scrimshaw, ...

New commits:

 ​4481ddf `Merge branch 'u/mshimo/combinat/double_affine_hecke_algebra' of git://trac.sagemath.org/sage into public/combinat/double_affine_hecke_algebra-17989` ​3f33aa3 `Removing some of the bitrot and doing some mild modernization.` ​bbb257d `Merge branch 'develop' into public/combinat/double_affine_hecke_algebra-17989`
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