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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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Table of 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.