Construct the composition series of Garsia-Procesi modules #37871
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Documentation preview for this PR (built with commit 34418b5; changes) is ready! 🎉 |
mkoeppe
reviewed
May 28, 2024
mkoeppe
reviewed
May 28, 2024
mkoeppe
reviewed
May 28, 2024
mkoeppe
reviewed
May 28, 2024
mkoeppe
reviewed
May 28, 2024
| """ | ||
| G = self._semigroup | ||
| B = self.basis() | ||
| chi = [sum((g * B[k])[k] for k in B.keys()) |
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perhaps
Suggested change
| chi = [sum((g * B[k])[k] for k in B.keys()) | |
| chi = [sum((g * b)[k] for k, b in B.items()) |
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I prefer the explicitness here, and I would like to keep it the way it is.
mkoeppe
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May 28, 2024
mkoeppe
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May 28, 2024
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I've made all the other changes. |
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Test failures. Looks like the rename |
Indeed, I missed one. Fixed. |
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vbraun
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sagemathgh-37871: Construct the composition series of Garsia-Procesi modules <!-- ^ 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". --> We provide an implementation of Garsia-Procesi modules, which are an important class of representations of the symmetric group that comes from the cohomology of the Springer fiber. This provides an implementation as a representation on a quotient ring. This also does the following as part of getting the code to work (and a few related changes): - Implement the meataxe algorithm over finite fields to compute the composition series. - Move the (Brauer) character and other methods from symmetric group representation to the general representation class. - Made the abstract representation class work more generically and streamlined the implementation. - Expose the `Representation` class as part of the semigroup (algebras) API. ### 📝 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: ... --> URL: sagemath#37871 Reported by: Travis Scrimshaw Reviewer(s): Matthias Köppe, Travis Scrimshaw
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Thank you. |
vbraun
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Jun 16, 2024
sagemathgh-37830: Implement the Schur functors applied to semigroup representations <!-- ^ 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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sagemathgh-37830: Implement the Schur functors applied to semigroup representations <!-- ^ 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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Jun 17, 2024
sagemathgh-37830: Implement the Schur functors applied to semigroup representations <!-- ^ 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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We provide an implementation of Garsia-Procesi modules, which are an important class of representations of the symmetric group that comes from the cohomology of the Springer fiber. This provides an implementation as a representation on a quotient ring. This also does the following as part of getting the code to work (and a few related changes):
Representationclass as part of the semigroup (algebras) API.📝 Checklist
⌛ Dependencies