Adding cellular bases for the SymmetricGroupAlgebra over general fields #36718
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@fchapoton I hope you can do the review for this. Mathematically it is just implementing the KL |
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there are a few failing doctests, some trivial and other less so |
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This should fix all of the failing doctests. They were all trivial coming from the fact that the cell poset was in the reverse order. |
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testing wihtout coxeter3 does not work: |
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Good catch. This should fix it. |
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Documentation preview for this PR (built with commit 2e492e9; changes) is ready! 🎉 |
fchapoton
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Nov 16, 2023
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Merci |
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<!-- ^^^^^ Please provide a concise, informative and self-explanatory title. Don't put issue numbers in there, do this in the PR body below. For example, instead of "Fixes sagemath#1234" use "Introduce new method to calculate 1+1" --> <!-- Describe your changes here in detail --> We implement the Murphy basis of the symmetric group algebra (as defined by Dipper-James-Mathas) and make this the default cellular basis over positive characteristic since it is (significantly) faster to compute the change of basis necessary. <!-- Why is this change required? What problem does it solve? --> <!-- If this PR resolves an open issue, please link to it here. For example "Fixes sagemath#12345". --> <!-- If your change requires a documentation PR, please link it appropriately. --> ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> <!-- If your change requires a documentation PR, please link it appropriately --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> <!-- Feel free to remove irrelevant items. --> - [x] The title is concise, informative, and self-explanatory. - [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 accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on - sagemath#12345: short description why this is a dependency - sagemath#34567: ... --> - sagemath#36718 Uses the KL basis implementation <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: sagemath#36790 Reported by: Travis Scrimshaw Reviewer(s): Frédéric Chapoton
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Dec 22, 2023
<!-- ^^^^^ Please provide a concise, informative and self-explanatory title. Don't put issue numbers in there, do this in the PR body below. For example, instead of "Fixes sagemath#1234" use "Introduce new method to calculate 1+1" --> <!-- Describe your changes here in detail --> We implement the Murphy basis of the symmetric group algebra (as defined by Dipper-James-Mathas) and make this the default cellular basis over positive characteristic since it is (significantly) faster to compute the change of basis necessary. <!-- Why is this change required? What problem does it solve? --> <!-- If this PR resolves an open issue, please link to it here. For example "Fixes sagemath#12345". --> <!-- If your change requires a documentation PR, please link it appropriately. --> ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> <!-- If your change requires a documentation PR, please link it appropriately --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> <!-- Feel free to remove irrelevant items. --> - [x] The title is concise, informative, and self-explanatory. - [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 accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on - sagemath#12345: short description why this is a dependency - sagemath#34567: ... --> - sagemath#36718 Uses the KL basis implementation <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: sagemath#36790 Reported by: Travis Scrimshaw Reviewer(s): Frédéric Chapoton
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Dec 23, 2023
<!-- ^^^^^ Please provide a concise, informative and self-explanatory title. Don't put issue numbers in there, do this in the PR body below. For example, instead of "Fixes sagemath#1234" use "Introduce new method to calculate 1+1" --> <!-- Describe your changes here in detail --> We implement the Murphy basis of the symmetric group algebra (as defined by Dipper-James-Mathas) and make this the default cellular basis over positive characteristic since it is (significantly) faster to compute the change of basis necessary. <!-- Why is this change required? What problem does it solve? --> <!-- If this PR resolves an open issue, please link to it here. For example "Fixes sagemath#12345". --> <!-- If your change requires a documentation PR, please link it appropriately. --> ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> <!-- If your change requires a documentation PR, please link it appropriately --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> <!-- Feel free to remove irrelevant items. --> - [x] The title is concise, informative, and self-explanatory. - [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 accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on - sagemath#12345: short description why this is a dependency - sagemath#34567: ... --> - sagemath#36718 Uses the KL basis implementation <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: sagemath#36790 Reported by: Travis Scrimshaw Reviewer(s): Frédéric Chapoton
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<!-- ^^^^^ Please provide a concise, informative and self-explanatory title. Don't put issue numbers in there, do this in the PR body below. For example, instead of "Fixes sagemath#1234" use "Introduce new method to calculate 1+1" --> <!-- Describe your changes here in detail --> We implement the Murphy basis of the symmetric group algebra (as defined by Dipper-James-Mathas) and make this the default cellular basis over positive characteristic since it is (significantly) faster to compute the change of basis necessary. <!-- Why is this change required? What problem does it solve? --> <!-- If this PR resolves an open issue, please link to it here. For example "Fixes sagemath#12345". --> <!-- If your change requires a documentation PR, please link it appropriately. --> ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> <!-- If your change requires a documentation PR, please link it appropriately --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> <!-- Feel free to remove irrelevant items. --> - [x] The title is concise, informative, and self-explanatory. - [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 accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on - sagemath#12345: short description why this is a dependency - sagemath#34567: ... --> - sagemath#36718 Uses the KL basis implementation <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: sagemath#36790 Reported by: Travis Scrimshaw Reviewer(s): Frédéric Chapoton
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<!-- ^^^^^ Please provide a concise, informative and self-explanatory title. Don't put issue numbers in there, do this in the PR body below. For example, instead of "Fixes sagemath#1234" use "Introduce new method to calculate 1+1" --> <!-- Describe your changes here in detail --> We implement the Murphy basis of the symmetric group algebra (as defined by Dipper-James-Mathas) and make this the default cellular basis over positive characteristic since it is (significantly) faster to compute the change of basis necessary. <!-- Why is this change required? What problem does it solve? --> <!-- If this PR resolves an open issue, please link to it here. For example "Fixes sagemath#12345". --> <!-- If your change requires a documentation PR, please link it appropriately. --> ### 📝 Checklist <!-- Put an `x` in all the boxes that apply. --> <!-- If your change requires a documentation PR, please link it appropriately --> <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> <!-- Feel free to remove irrelevant items. --> - [x] The title is concise, informative, and self-explanatory. - [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 accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on - sagemath#12345: short description why this is a dependency - sagemath#34567: ... --> - sagemath#36718 Uses the KL basis implementation <!-- If you're unsure about any of these, don't hesitate to ask. We're here to help! --> URL: sagemath#36790 Reported by: Travis Scrimshaw Reviewer(s): Frédéric Chapoton
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Currently the SymmetricGroupAlgebra uses the seminormal basis for computing a cell basis, but this only is guaranteed to work over a field where Maschke's theorem holds. However, it is known that the Kazhdan-Lusztig C' basis at q = 1 for the type A Hecke algebra is a cell basis, We implement that as the fallback when we cannot use the seminormal basis.
We also fix a few typos in the doc that were noticed.
📝 Checklist
⌛ Dependencies