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Eigenweights for arithmetic Hirzebruch Proportionality
1Mathematics Department, University of California, Berkeley, CA 94720 USA.
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, 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.
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