Eigenweights for arithmetic Hirzebruch Proportionality
Fuente:
arXiv
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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866910008330944512 |
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| author | Feng, Tony |
| author_facet | Feng, Tony |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_23245 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eigenweights for arithmetic Hirzebruch Proportionality Feng, Tony Representation Theory Number Theory 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. |
| title | Eigenweights for arithmetic Hirzebruch Proportionality |
| topic | Representation Theory Number Theory |
| url | https://arxiv.org/abs/2601.23245 |