Cores and weights of multipartitions and blocks of Ariki-Koike algebras
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915104893698048 |
|---|---|
| author | Li, Yanbo Tan, Kai Meng |
| author_facet | Li, Yanbo Tan, Kai Meng |
| contents | Let $e$ be an integer at least two. We define the $e$-core and the $e$-weight of a multipartition associated with a multicharge as the $e$-core and the $e$-weight of its image under the Uglov map. We do not place any restriction on the multicharge for these definitions. We show how these definitions lead to the definition of the $e$-core and the $e$-weight of a block of an Ariki-Koike algebra with quantum parameter $e$, and an analogue of Nakayama's `Conjecture' that classifies these blocks. Our definition of $e$-weight of such a block coincides with that first defined by Fayers. We further generalise the notion of a $[w:k]$-pair for Iwahori-Hecke algebra of type $A$ to the Ariki-Koike algebras, and obtain a sufficient condition for such a pair to be Scopes equivalent. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_10626 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Cores and weights of multipartitions and blocks of Ariki-Koike algebras Li, Yanbo Tan, Kai Meng Representation Theory 20C08, 05E10 Let $e$ be an integer at least two. We define the $e$-core and the $e$-weight of a multipartition associated with a multicharge as the $e$-core and the $e$-weight of its image under the Uglov map. We do not place any restriction on the multicharge for these definitions. We show how these definitions lead to the definition of the $e$-core and the $e$-weight of a block of an Ariki-Koike algebra with quantum parameter $e$, and an analogue of Nakayama's `Conjecture' that classifies these blocks. Our definition of $e$-weight of such a block coincides with that first defined by Fayers. We further generalise the notion of a $[w:k]$-pair for Iwahori-Hecke algebra of type $A$ to the Ariki-Koike algebras, and obtain a sufficient condition for such a pair to be Scopes equivalent. |
| title | Cores and weights of multipartitions and blocks of Ariki-Koike algebras |
| topic | Representation Theory 20C08, 05E10 |
| url | https://arxiv.org/abs/2408.10626 |