Equivalence of $v$-decomposition matrices for blocks of Ariki-Koike algebras
Fuente:
arXiv
Guardado en:
| Autor principal: | |
|---|---|
| Formato: | Preprint |
| Publicado: |
2023
|
| Materias: | |
| Acceso en línea: | |
| Etiquetas: |
Agregar Etiqueta
Sin Etiquetas, Sea el primero en etiquetar este registro!
|
| _version_ | 1866929249547452416 |
|---|---|
| author | Dell'Arciprete, Alice |
| author_facet | Dell'Arciprete, Alice |
| contents | We consider the representation theory of the Ariki-Koike algebra, a $q$-deformation of the group algebra of the complex reflection group $C_r \wr \mathfrak{S}_n$. We examine blocks of the Ariki-Koike algebra. In particular, we prove a sufficient condition such that restriction of modules leads to a natural correspondence between the multipartitions of $n$ whose Specht modules belong to a block $B$ and those of $n-δ_i(B)$ whose Specht modules belong to the block $B'$, obtained from $B$ applying a Scopes' equivalence. This bijection gives us an equivalence for the $v$-decomposition numbers of the Ariki-Koike algebras. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2301_05153 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Equivalence of $v$-decomposition matrices for blocks of Ariki-Koike algebras Dell'Arciprete, Alice Representation Theory 20C08, 20C30, 05E10 We consider the representation theory of the Ariki-Koike algebra, a $q$-deformation of the group algebra of the complex reflection group $C_r \wr \mathfrak{S}_n$. We examine blocks of the Ariki-Koike algebra. In particular, we prove a sufficient condition such that restriction of modules leads to a natural correspondence between the multipartitions of $n$ whose Specht modules belong to a block $B$ and those of $n-δ_i(B)$ whose Specht modules belong to the block $B'$, obtained from $B$ applying a Scopes' equivalence. This bijection gives us an equivalence for the $v$-decomposition numbers of the Ariki-Koike algebras. |
| title | Equivalence of $v$-decomposition matrices for blocks of Ariki-Koike algebras |
| topic | Representation Theory 20C08, 20C30, 05E10 |
| url | https://arxiv.org/abs/2301.05153 |