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gh-37619: Implement the Potts representation of the partition algebra <!-- ^ 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 #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 #12345". --> The Potts representation is an important representation of the partition algebra $P_n(d)$ (say, over a field of characteristic 0) that corresponds to the Schur-Weyl duality with the symmetric group $S_d$. We provide an implementation of this representation, both as a left $S_d$-module and right $P_n(d)$-module. (If $n$ is a half integer, then we only have a $S_{d-1}$-module.) ### 📝 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 accordingly. ### ⌛ Dependencies <!-- List all open PRs that this PR logically depends on. For example, --> <!-- - #12345: short description why this is a dependency --> <!-- - #34567: ... --> URL: #37619 Reported by: Travis Scrimshaw Reviewer(s): Frédéric Chapoton
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src/doc/en/reference/references/index.rst

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@@ -4823,6 +4823,11 @@ REFERENCES:
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Journal of Algebra 177 (1995), no. 3, 967-982.
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http://www.lacim.uqam.ca/~christo/Publi%C3%A9s/1995/Duality.pdf
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.. [MR1998] \P. P. Martin and G. Rollet.
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*The Potts model representation and a Robinson-Schensted
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correspondence for the partition algebra*.
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Compositio Math., **112** (1998), pp. 237-254.
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.. [MR2002] \S. Murphy, M. Robshaw *Essential Algebraic Structure
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Within the AES*; in Advances in Cryptology \- CRYPTO
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2002; LNCS 2442; Springer Verlag 2002

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