Year: 2026
Type: preprint
Abstract: 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.
Source: arXiv (Cornell University)
Authors: Kamgarpour, Masoud, Whitbread, Bailey
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7140180889
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