Eigenweights for arithmetic Hirzebruch Proportionality
Abstract
Abstract Prior work of Feng–Yun–Zhang established a (Higher) Arithmetic Hirzebruch Proportionality Principle, expressing the arithmetic volumes of moduli stacks of shtukas in terms of differential operators applied to L-functions. This formula involves certain “eigenweights” which were calculated in simple cases by Feng–Yun–Zhang, but not in general. We document work of a (custom) AI Agent codenamed Aletheia,a built upon Gemini Deep Think, which employs tools from algebraic combinatorics to connect these eigenweights to the representation theory of symmetric groups and then determines them for all classical groups.
Fields of Study & Subjects
Advanced Algebra and Geometry
Homotopy and Cohomology in Algebraic Topology
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- PNAS Nexus
- Publisher
- Oxford University Press (OUP)
- Volume
- 5
- Issue
- 5
- Pages
- pgag143–pgag143
- Publication date
- 30 April 2026
- Language
- EN