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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2505.05910 |
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| _version_ | 1866912431327936512 |
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| author | Idrissi, Najib Lindell, Erik |
| author_facet | Idrissi, Najib Lindell, Erik |
| contents | We investigate the relationship between symmetric functions and the representation theory of operads, relative operads, and props. We extend the classical character map for symmetric sequences to relative bisymmetric sequences and symmetric bimodules. We introduce new operations on symmetric functions, the relative plethysm and the (connected) box product, which model via the character map the composition product of relative operads and the box product of prop(erad)s. As applications, we include the computation of characters for stable twisted cohomology of automorphism groups of free groups and the Albanese cohomology of the IA-automorphism group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_05910 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Plethysm for characters of relative operads and PROPs Idrissi, Najib Lindell, Erik Algebraic Topology 05E05, 18M60, 20F28 We investigate the relationship between symmetric functions and the representation theory of operads, relative operads, and props. We extend the classical character map for symmetric sequences to relative bisymmetric sequences and symmetric bimodules. We introduce new operations on symmetric functions, the relative plethysm and the (connected) box product, which model via the character map the composition product of relative operads and the box product of prop(erad)s. As applications, we include the computation of characters for stable twisted cohomology of automorphism groups of free groups and the Albanese cohomology of the IA-automorphism group. |
| title | Plethysm for characters of relative operads and PROPs |
| topic | Algebraic Topology 05E05, 18M60, 20F28 |
| url | https://arxiv.org/abs/2505.05910 |