Full runner removal theorem for Ariki-Koike algebras
Fuente:
arXiv
Enregistré dans:
| Auteur principal: | |
|---|---|
| Format: | Preprint |
| Publié: |
2023
|
| Sujets: | |
| Accès en ligne: | |
| Tags: |
Ajouter un tag
Pas de tags, Soyez le premier à ajouter un tag!
|
| _version_ | 1866916338991104000 |
|---|---|
| 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 $C_r \wr S_n$. We define the addition of a runner full of beads for the abacus display of a multipartition and investigate some combinatorial properties of this operation. We focus our attention on the $q$-decomposition numbers, i.e. the polynomials arising from the Fock space representation of the quantum group $U_q(\widehat{\mathfrak{sl}}_e)$. Using Fayers' LLT-type algorithm for Ariki-Koike algebras, we relate $q$-decomposition numbers for different values of $e$ for the class of $e$-multiregular multipartitions, by adding a full runner of beads to each component of the abacus displays for the labelling multipartitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2310_08156 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Full runner removal theorem for Ariki-Koike algebras Dell'Arciprete, Alice Representation Theory Combinatorics We consider the representation theory of the Ariki-Koike algebra, a $q$-deformation of the group algebra of the complex reflection group $C_r \wr S_n$. We define the addition of a runner full of beads for the abacus display of a multipartition and investigate some combinatorial properties of this operation. We focus our attention on the $q$-decomposition numbers, i.e. the polynomials arising from the Fock space representation of the quantum group $U_q(\widehat{\mathfrak{sl}}_e)$. Using Fayers' LLT-type algorithm for Ariki-Koike algebras, we relate $q$-decomposition numbers for different values of $e$ for the class of $e$-multiregular multipartitions, by adding a full runner of beads to each component of the abacus displays for the labelling multipartitions. |
| title | Full runner removal theorem for Ariki-Koike algebras |
| topic | Representation Theory Combinatorics |
| url | https://arxiv.org/abs/2310.08156 |