Tensor Product Decompositions, Limits in Excellent Filtrations, Affine Weyl Group Orbits, and Tableaux Counting
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911193929613312 |
|---|---|
| author | Estivalez, Laura Moura, Adriano |
| author_facet | Estivalez, Laura Moura, Adriano |
| contents | We express the outer multiplicities in the tensor products of two fundamental simple modules for an affine Kac-Moody algebra of type $A$ in terms of counting certain sets of multipartitions by exploring the stabilizing limits of certain excellent filtrations. This extends for all ranks a previously obtained result by Jakelić and the second author for rank $1$. The same outer multiplicities were previously computed by Misra and Wilson in terms of counting certain sets of tableaux. By comparing these two expressions and by explicitly exhibiting a combinatorial description of level-$2$ affine Weyl group orbits, we establish the existence of a bijection between the Misra-Wilson set of tableaux and a disjoint union of certain sets of multipartitions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_04697 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tensor Product Decompositions, Limits in Excellent Filtrations, Affine Weyl Group Orbits, and Tableaux Counting Estivalez, Laura Moura, Adriano Representation Theory Combinatorics 17B10, 17B67, 05E10, 05A17, 05A19, 20G42, 81R10 We express the outer multiplicities in the tensor products of two fundamental simple modules for an affine Kac-Moody algebra of type $A$ in terms of counting certain sets of multipartitions by exploring the stabilizing limits of certain excellent filtrations. This extends for all ranks a previously obtained result by Jakelić and the second author for rank $1$. The same outer multiplicities were previously computed by Misra and Wilson in terms of counting certain sets of tableaux. By comparing these two expressions and by explicitly exhibiting a combinatorial description of level-$2$ affine Weyl group orbits, we establish the existence of a bijection between the Misra-Wilson set of tableaux and a disjoint union of certain sets of multipartitions. |
| title | Tensor Product Decompositions, Limits in Excellent Filtrations, Affine Weyl Group Orbits, and Tableaux Counting |
| topic | Representation Theory Combinatorics 17B10, 17B67, 05E10, 05A17, 05A19, 20G42, 81R10 |
| url | https://arxiv.org/abs/2510.04697 |