Cocharacters of generalized polynomial identities
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866909716120076288 |
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| author | Argenti, Sebastiano Busalacchi, Giovanni |
| author_facet | Argenti, Sebastiano Busalacchi, Giovanni |
| contents | In this paper we extend the cocharacter theory to generalized identities of $W$-algebras. We prove that the Hilbert series of the relatively free $W$-algebra admits an expansion in terms of Schur functions whose coefficients coincide with generalized cocharacter multiplicities. Moreover, we prove analogues of the Hook and Strip theorems for $W$-algebras and we derive growth bounds for generalized codimension and colenght sequences. Finally, we establish that every variety $\mathcal{V}$ of $W$-algebras is generated by the Grassmann envelope of a finitely generated $W$-superalgebra, and if $\mathcal{V}$ satisfies a generalized Capelli set, then it is generated by a finitely generated $W$-algebra. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_00464 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cocharacters of generalized polynomial identities Argenti, Sebastiano Busalacchi, Giovanni Rings and Algebras Primary 16R10, 16R50, Secondary 16W99 In this paper we extend the cocharacter theory to generalized identities of $W$-algebras. We prove that the Hilbert series of the relatively free $W$-algebra admits an expansion in terms of Schur functions whose coefficients coincide with generalized cocharacter multiplicities. Moreover, we prove analogues of the Hook and Strip theorems for $W$-algebras and we derive growth bounds for generalized codimension and colenght sequences. Finally, we establish that every variety $\mathcal{V}$ of $W$-algebras is generated by the Grassmann envelope of a finitely generated $W$-superalgebra, and if $\mathcal{V}$ satisfies a generalized Capelli set, then it is generated by a finitely generated $W$-algebra. |
| title | Cocharacters of generalized polynomial identities |
| topic | Rings and Algebras Primary 16R10, 16R50, Secondary 16W99 |
| url | https://arxiv.org/abs/2508.00464 |