Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2306.08857 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866909508828135424 |
|---|---|
| author | Gossow, Fern Yacobi, Oded |
| author_facet | Gossow, Fern Yacobi, Oded |
| contents | We study representations of simply-laced Weyl groups which are equipped with canonical bases. Our main result is that for a large class of representations, the separable elements of the Weyl group $W$ act on these canonical bases by bijections up to lower-order terms. Examples of this phenomenon include the action of separable permutations on the Kazhdan--Lusztig basis of irreducible representations for the symmetric group, and the action of separable elements of $W$ on dual canonical bases of weight zero in tensor product representations of a Lie algebra. Our methods arise from categorical representation theory, and in particular the study of the perversity of Rickard complexes acting on triangulated categories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_08857 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On the action of the Weyl group on canonical bases Gossow, Fern Yacobi, Oded Representation Theory Combinatorics 05E10 (Primary), 18N25 (Secondary) We study representations of simply-laced Weyl groups which are equipped with canonical bases. Our main result is that for a large class of representations, the separable elements of the Weyl group $W$ act on these canonical bases by bijections up to lower-order terms. Examples of this phenomenon include the action of separable permutations on the Kazhdan--Lusztig basis of irreducible representations for the symmetric group, and the action of separable elements of $W$ on dual canonical bases of weight zero in tensor product representations of a Lie algebra. Our methods arise from categorical representation theory, and in particular the study of the perversity of Rickard complexes acting on triangulated categories. |
| title | On the action of the Weyl group on canonical bases |
| topic | Representation Theory Combinatorics 05E10 (Primary), 18N25 (Secondary) |
| url | https://arxiv.org/abs/2306.08857 |