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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.04124 |
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| _version_ | 1866911311088058368 |
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| author | Keidar, Shai Ragimov, Shaul |
| author_facet | Keidar, Shai Ragimov, Shaul |
| contents | We study a class of representations of symmetric groups in higher semiadditive categories. For these representations in $\mathrm{Mod}^{\wedge}_{E_n}$, the transchromatic character of Hopkins--Kuhn--Ravenel and Stapleton is recovered as a sequence of monoidal characters on suitable categorifications, giving an explicit algorithm for its computation, and relating it to the iterated monoidal character in $(\infty,n)$-categories. These representations also give rise to notions of alternating powers and power operations in semiadditive categories, extending the classical alternating powers and $λ$-operations in $\mathrm{K}$-theory. We provide explicit computations in both the chromatic and higher categorical settings at low heights. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04124 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Semiadditive Alternating Powers and Twisted Power Operation Keidar, Shai Ragimov, Shaul Algebraic Topology We study a class of representations of symmetric groups in higher semiadditive categories. For these representations in $\mathrm{Mod}^{\wedge}_{E_n}$, the transchromatic character of Hopkins--Kuhn--Ravenel and Stapleton is recovered as a sequence of monoidal characters on suitable categorifications, giving an explicit algorithm for its computation, and relating it to the iterated monoidal character in $(\infty,n)$-categories. These representations also give rise to notions of alternating powers and power operations in semiadditive categories, extending the classical alternating powers and $λ$-operations in $\mathrm{K}$-theory. We provide explicit computations in both the chromatic and higher categorical settings at low heights. |
| title | Semiadditive Alternating Powers and Twisted Power Operation |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2507.04124 |