Counting points on braid varieties and the Deligne--Simpson problem
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2026
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866911532808404992 |
|---|---|
| author | Kamgarpour, Masoud Whitbread, Bailey |
| author_facet | Kamgarpour, Masoud Whitbread, Bailey |
| contents | We solve the isoclinic Deligne--Simpson problem for exceptional groups, completing a program initiated by Sage et al. and Jakob--Yun. As a by-product, we obtain new examples of physically rigid irregular connections on the projective line. Our approach uses the Riemann--Hilbert correspondence to reduce the problem to determining the non-emptiness of certain braid varieties associated to periodic braids. We show that this can be achieved by counting points over finite fields. Our approach is inspired by Lusztig's construction of a map from conjugacy classes in the Weyl group to unipotent classes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20499 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Counting points on braid varieties and the Deligne--Simpson problem Kamgarpour, Masoud Whitbread, Bailey Algebraic Geometry Representation Theory We solve the isoclinic Deligne--Simpson problem for exceptional groups, completing a program initiated by Sage et al. and Jakob--Yun. As a by-product, we obtain new examples of physically rigid irregular connections on the projective line. Our approach uses the Riemann--Hilbert correspondence to reduce the problem to determining the non-emptiness of certain braid varieties associated to periodic braids. We show that this can be achieved by counting points over finite fields. Our approach is inspired by Lusztig's construction of a map from conjugacy classes in the Weyl group to unipotent classes. |
| title | Counting points on braid varieties and the Deligne--Simpson problem |
| topic | Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2603.20499 |