Hall monoidal categories and categorical modules
| Autor: | Walde, Tashi |
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| Rok vydání: | 2016 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | We construct so called Hall monoidal categories (and Hall modules thereover) and exhibit them as a categorification of classical Hall and Hecke algebras (and certain modules thereover). The input of the (functorial!) construction are simplicial groupoids satisfying the $2$-Segal conditions (as introduced by Dyckerhoff and Kapranov), the main examples come from Waldhausen's S-construction. To treat the case of modules, we introduce a relative version of the $2$-Segal conditions. Furthermore, we generalize a classical result about the representation theory of symmetric groups to the case of wreath product groups: We construct a monoidal equivalence between the category of complex $G\wr S_n$-representations (for a fixed finite group $G$ and varying $n\in\mathbb N$) and the category of "$G$-equivariant" polynomial functors; we use this equivalence to prove a version of Schur-Weyl duality for wreath products. Comment: This paper is, up to minor modifications, the author's Master's thesis as submitted to the University of Bonn on July 22, 2016. v2: added missing LaTeX files, added references and remarks, minor changes to terminology in Section 4.1 |
| Databáze: | arXiv |
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