RSK as a linear operator
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866910756745773056 |
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| author | Stelzer, Ada Yong, Alexander |
| author_facet | Stelzer, Ada Yong, Alexander |
| contents | The Robinson-Schensted-Knuth correspondence (RSK) is a bijection between nonnegative integer matrices and pairs of Young tableaux. We study it as a linear operator on the coordinate ring of matrices, proving results about its diagonalizability, eigenvalues, trace, and determinant. Our criterion for diagonalizability involves the $ADE$ classification of Dynkin diagrams, as well as the diagram for $E_9$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_23009 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | RSK as a linear operator Stelzer, Ada Yong, Alexander Rings and Algebras Combinatorics Representation Theory The Robinson-Schensted-Knuth correspondence (RSK) is a bijection between nonnegative integer matrices and pairs of Young tableaux. We study it as a linear operator on the coordinate ring of matrices, proving results about its diagonalizability, eigenvalues, trace, and determinant. Our criterion for diagonalizability involves the $ADE$ classification of Dynkin diagrams, as well as the diagram for $E_9$. |
| title | RSK as a linear operator |
| topic | Rings and Algebras Combinatorics Representation Theory |
| url | https://arxiv.org/abs/2410.23009 |