Implement the Schur functors applied to semigroup representations #37830
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Documentation preview for this PR (built with commit ee80187; changes) is ready! 🎉 |
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mkoeppe
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Jun 4, 2024
mkoeppe
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Jun 4, 2024
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I am planning to rebase this over #37871 since that reworks the class hierarchy that this code depends on. I am going to try to do that today before going home, but it might have to wait until tomorrow. |
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It went much more smoothly than I thought (which is a good thing). |
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rebase again? |
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I didn't need to do it locally it seems, but I have done so. |
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Thank you. |
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…epresentations
<!-- ^ Please provide a concise and informative title. -->
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
<!-- v Why is this change required? What problem does it solve? -->
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes sagemath#12345". -->
The Schur functor is an important part of the representation theory of
$GL_n$, but it can be defined generically for any representation of a
semigroup (well, really for any vector space, but the utility is for
representation theory). We provide an implementation, realizing the
natural representation structure. To help with examples, we also
implement the natural representation of any matrix (semi)group.
Along the way, we clean up some stuff with the sign representations.
### 📝 Checklist
<!-- Put an `x` in all the boxes that apply. -->
- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation and checked the documentation
preview.
### ⌛ Dependencies
<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->
- sagemath#37871 - Uses the `Subrepresentation` class implemented here.
URL: sagemath#37830
Reported by: Travis Scrimshaw
Reviewer(s): Matthias Köppe
vbraun
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…epresentations
<!-- ^ Please provide a concise and informative title. -->
<!-- ^ Don't put issue numbers in the title, do this in the PR
description below. -->
<!-- ^ For example, instead of "Fixes sagemath#12345" use "Introduce new method
to calculate 1 + 2". -->
<!-- v Describe your changes below in detail. -->
<!-- v Why is this change required? What problem does it solve? -->
<!-- v If this PR resolves an open issue, please link to it here. For
example, "Fixes sagemath#12345". -->
The Schur functor is an important part of the representation theory of
$GL_n$, but it can be defined generically for any representation of a
semigroup (well, really for any vector space, but the utility is for
representation theory). We provide an implementation, realizing the
natural representation structure. To help with examples, we also
implement the natural representation of any matrix (semi)group.
Along the way, we clean up some stuff with the sign representations.
### 📝 Checklist
<!-- Put an `x` in all the boxes that apply. -->
- [x] The title is concise and informative.
- [x] The description explains in detail what this PR is about.
- [x] I have linked a relevant issue or discussion.
- [x] I have created tests covering the changes.
- [x] I have updated the documentation and checked the documentation
preview.
### ⌛ Dependencies
<!-- List all open PRs that this PR logically depends on. For example,
-->
<!-- - sagemath#12345: short description why this is a dependency -->
<!-- - sagemath#34567: ... -->
- sagemath#37871 - Uses the `Subrepresentation` class implemented here.
URL: sagemath#37830
Reported by: Travis Scrimshaw
Reviewer(s): Matthias Köppe
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The Schur functor is an important part of the representation theory of$GL_n$ , but it can be defined generically for any representation of a semigroup (well, really for any vector space, but the utility is for representation theory). We provide an implementation, realizing the natural representation structure. To help with examples, we also implement the natural representation of any matrix (semi)group.
Along the way, we clean up some stuff with the sign representations.
📝 Checklist
⌛ Dependencies
Subrepresentationclass implemented here.