Eigenforms and graphs of Hecke operators with wild ramification
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866908994800451584 |
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| author | Kashyap, Rudrendra Zveryk, Vladyslav |
| author_facet | Kashyap, Rudrendra Zveryk, Vladyslav |
| contents | Hecke operators on moduli of bundles over a global function field become substantially more complicated in the presence of ramification. We show that far enough in the Harder-Narasimhan cone of $\mathrm{Bun}_G$, this extra complexity has a simple structure, which allows to reduce most of the study to the unramified case. Using the theory of graphs of Hecke operators, we transform this statement into a combinatorial condition. Utilizing the combinatorial language, we obtain tight bounds, and for generic eigenvalues exact formulas for the dimensions of Hecke eigenspaces with arbitrary ramification for $\mathrm{Bun}_{\mathrm{PGL}_2}$. Moreover, our methods allow to construct eigenforms explicitly. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15931 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Eigenforms and graphs of Hecke operators with wild ramification Kashyap, Rudrendra Zveryk, Vladyslav Algebraic Geometry Number Theory Representation Theory Hecke operators on moduli of bundles over a global function field become substantially more complicated in the presence of ramification. We show that far enough in the Harder-Narasimhan cone of $\mathrm{Bun}_G$, this extra complexity has a simple structure, which allows to reduce most of the study to the unramified case. Using the theory of graphs of Hecke operators, we transform this statement into a combinatorial condition. Utilizing the combinatorial language, we obtain tight bounds, and for generic eigenvalues exact formulas for the dimensions of Hecke eigenspaces with arbitrary ramification for $\mathrm{Bun}_{\mathrm{PGL}_2}$. Moreover, our methods allow to construct eigenforms explicitly. |
| title | Eigenforms and graphs of Hecke operators with wild ramification |
| topic | Algebraic Geometry Number Theory Representation Theory |
| url | https://arxiv.org/abs/2603.15931 |