The circular Delannoy category
| Autor: | Harman, Nate, Snowden, Andrew, Snyder, Noah |
|---|---|
| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $G$ (resp. $H$) be the group of orientation preserving self-homeomorphisms of the unit circle (resp. real line). In previous work, the first two authors constructed pre-Tannakian categories $\underline{\mathrm{Rep}}(G)$ and $\underline{\mathrm{Rep}}(H)$ associated to these groups. In the predecessor to this paper, we analyzed the category $\underline{\mathrm{Rep}}(H)$ (which we named the ``Delannoy category'') in great detail, and found it to have many special properties. In this paper, we study $\underline{\mathrm{Rep}}(G)$. The primary difference between these two categories is that $\underline{\mathrm{Rep}}(H)$ is semi-simple, while $\underline{\mathrm{Rep}}(G)$ is not; this introduces new complications in the present case. We find that $\underline{\mathrm{Rep}}(G)$ is closely related to the combinatorics of objects we call Delannoy loops, which seem to have not previously been studied. Comment: 38 pages |
| Databáze: | arXiv |
| Externí odkaz: |
|