On the free LAnKe on $3n-2$ generators: a theorem of Friedmann, Hanlon, Stanley and Wachs
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914569951117312 |
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| author | Maliakas, Mihalis Stergiopoulou, Dimitra-Dionysia |
| author_facet | Maliakas, Mihalis Stergiopoulou, Dimitra-Dionysia |
| contents | A LAnKe (also known as a Filippov algebra or a Lie algebra of the $n$-th kind) is a vector space equipped with a skew-symmetric $n$-linear form that satisfies the generalized Jacobi identity. Friedmann, Hanlon, Stanley and Wachs have shown that the symmetric group acts on the multilinear part of the free LAnKe on $2n-1$ generators as an irreducible representation. They announced that the multilinear component on $3n-2$ generators decomposes as a direct sum of two irreducible symmetric group representations and a proof was given recently in a subsequent paper by Friedmann, Hanlon and Wachs. In the present paper we provide a proof of the later statement. The two proofs are substantially different. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09405 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the free LAnKe on $3n-2$ generators: a theorem of Friedmann, Hanlon, Stanley and Wachs Maliakas, Mihalis Stergiopoulou, Dimitra-Dionysia Representation Theory Combinatorics 05E10, 20C30, 20G05 A LAnKe (also known as a Filippov algebra or a Lie algebra of the $n$-th kind) is a vector space equipped with a skew-symmetric $n$-linear form that satisfies the generalized Jacobi identity. Friedmann, Hanlon, Stanley and Wachs have shown that the symmetric group acts on the multilinear part of the free LAnKe on $2n-1$ generators as an irreducible representation. They announced that the multilinear component on $3n-2$ generators decomposes as a direct sum of two irreducible symmetric group representations and a proof was given recently in a subsequent paper by Friedmann, Hanlon and Wachs. In the present paper we provide a proof of the later statement. The two proofs are substantially different. |
| title | On the free LAnKe on $3n-2$ generators: a theorem of Friedmann, Hanlon, Stanley and Wachs |
| topic | Representation Theory Combinatorics 05E10, 20C30, 20G05 |
| url | https://arxiv.org/abs/2401.09405 |