Cellular subalgebras of the partition algebra
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866916156052340736 |
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| author | Scrimshaw, Travis |
| author_facet | Scrimshaw, Travis |
| contents | We describe various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we show the diagram algebras surveyed here are all cellular algebras and parameterize their cell modules. We give a new construction to build new cellular algebras from a general cellular algebra and subalgebras of the rook Brauer algebra that we call the cellular wreath product. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_08746 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Cellular subalgebras of the partition algebra Scrimshaw, Travis Representation Theory Combinatorics Rings and Algebras 05E10, 16G99, 05E16, 05A19 We describe various diagram algebras and their representation theory using cellular algebras of Graham and Lehrer and the decomposition into half diagrams. In particular, we show the diagram algebras surveyed here are all cellular algebras and parameterize their cell modules. We give a new construction to build new cellular algebras from a general cellular algebra and subalgebras of the rook Brauer algebra that we call the cellular wreath product. |
| title | Cellular subalgebras of the partition algebra |
| topic | Representation Theory Combinatorics Rings and Algebras 05E10, 16G99, 05E16, 05A19 |
| url | https://arxiv.org/abs/2211.08746 |