Eigenweights for arithmetic Hirzebruch Proportionality

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*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.