Empty runner removal theorem for Ariki-Koike algebras
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
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| _version_ | 1866913014213509120 |
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| author | Dell'Arciprete, Alice Putignano, Lorenzo |
| author_facet | Dell'Arciprete, Alice Putignano, Lorenzo |
| contents | For the Iwahori-Hecke algebras of type $A$, James and Mathas proved a theorem which relates $v$-decomposition numbers for different values of $e$, by adding empty runners to the James' abacus display. This result is often referred to as the empty runner removal theorem. In this paper, we extend this theorem to the Ariki-Koike algebras, establishing a similar relationship for the $v$-decomposition numbers. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_08811 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Empty runner removal theorem for Ariki-Koike algebras Dell'Arciprete, Alice Putignano, Lorenzo Representation Theory For the Iwahori-Hecke algebras of type $A$, James and Mathas proved a theorem which relates $v$-decomposition numbers for different values of $e$, by adding empty runners to the James' abacus display. This result is often referred to as the empty runner removal theorem. In this paper, we extend this theorem to the Ariki-Koike algebras, establishing a similar relationship for the $v$-decomposition numbers. |
| title | Empty runner removal theorem for Ariki-Koike algebras |
| topic | Representation Theory |
| url | https://arxiv.org/abs/2506.08811 |