Representation stability and outer automorphism groups
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2021
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| _version_ | 1866916626230673408 |
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| author | Pol, Luca Strickland, Neil P. |
| author_facet | Pol, Luca Strickland, Neil P. |
| contents | In this paper we study families of representations of the outer automorphism groups indexed on a collection of finite groups $\mathcal{U}$. We encode this large amount of data into a convenient abelian category $\mathcal{A}\mathcal{U}$ which generalizes the category of VI-modules appearing in the representation theory of the finite general linear groups. Inspired by work of Church--Ellenberg--Farb, we investigate for which choices of $\mathcal{U}$ the abelian category is locally noetherian and deduce analogues of central stability and representation stability results in this setting. Finally, we show that some invariants coming from rational global homotopy theory exhibit representation stability. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2102_06410 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Representation stability and outer automorphism groups Pol, Luca Strickland, Neil P. Representation Theory Algebraic Topology Category Theory 05E10, 20J05, 55P91 In this paper we study families of representations of the outer automorphism groups indexed on a collection of finite groups $\mathcal{U}$. We encode this large amount of data into a convenient abelian category $\mathcal{A}\mathcal{U}$ which generalizes the category of VI-modules appearing in the representation theory of the finite general linear groups. Inspired by work of Church--Ellenberg--Farb, we investigate for which choices of $\mathcal{U}$ the abelian category is locally noetherian and deduce analogues of central stability and representation stability results in this setting. Finally, we show that some invariants coming from rational global homotopy theory exhibit representation stability. |
| title | Representation stability and outer automorphism groups |
| topic | Representation Theory Algebraic Topology Category Theory 05E10, 20J05, 55P91 |
| url | https://arxiv.org/abs/2102.06410 |