A continuous associahedron of type A
Fuente:
arXiv
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| Autores principales: | , , , |
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| Formato: | Preprint |
| Publicado: |
2021
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866908682313269248 |
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| author | Kulkarni, Maitreyee C. Matherne, Jacob P. Mousavand, Kaveh Rock, Job D. |
| author_facet | Kulkarni, Maitreyee C. Matherne, Jacob P. Mousavand, Kaveh Rock, Job D. |
| contents | Taking a representation-theoretic viewpoint, we construct a continuous associahedron motivated by the realization of the generalized associahedron in the physical setting. We show that our associahedron shares important properties with the generalized associahedron of type A. Our continuous associahedron is convex and manifests a cluster theory: the points which correspond to the clusters are on its boundary, and the edges that correspond to mutations are given by intersections of hyperplanes. This requires development of several methods that are continuous analogues of discrete methods. We conclude the paper by showing that there is a sequence of embeddings of type A generalized associahedra into our continuous associahedron. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_12927 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | A continuous associahedron of type A Kulkarni, Maitreyee C. Matherne, Jacob P. Mousavand, Kaveh Rock, Job D. Representation Theory High Energy Physics - Theory Combinatorics Category Theory 16G20, 18G80 (primary), 13F60, 05E10 (secondary) Taking a representation-theoretic viewpoint, we construct a continuous associahedron motivated by the realization of the generalized associahedron in the physical setting. We show that our associahedron shares important properties with the generalized associahedron of type A. Our continuous associahedron is convex and manifests a cluster theory: the points which correspond to the clusters are on its boundary, and the edges that correspond to mutations are given by intersections of hyperplanes. This requires development of several methods that are continuous analogues of discrete methods. We conclude the paper by showing that there is a sequence of embeddings of type A generalized associahedra into our continuous associahedron. |
| title | A continuous associahedron of type A |
| topic | Representation Theory High Energy Physics - Theory Combinatorics Category Theory 16G20, 18G80 (primary), 13F60, 05E10 (secondary) |
| url | https://arxiv.org/abs/2108.12927 |