The spherical Hall algebra of $\overline{\operatorname{Spec}(\mathcal{O}_K)}$

Benjamin Li; Luis Modes

The spherical Hall algebra of $\overline{\operatorname{Spec}(\mathcal{O}_K)}$

Number Theory 2024-11-27 v1 Algebraic Geometry

Authors: Benjamin Li , Luis Modes

Abstract

We generalize a result of M. Kapranov, O. Schiffmann, and E. Vasserot by showing that, for a number field $K$ with class number one, the spherical Hall algebra of $\overline{\operatorname{Spec}(\mathcal{O}_K)}$ , where $\mathcal{O}_K$ is the ring of integers of $K$ , is isomorphic to the Paley-Wiener shuffle algebra associated to a Hecke $L$ -function corresponding to $K$ .

Keywords

spherical Hall algebra number field Paley-Wiener shuffle algebra Hecke L-function class number

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@article{arxiv.2411.17055,
  title  = {The spherical Hall algebra of $\overline{\operatorname{Spec}(\mathcal{O}_K)}$},
  author = {Benjamin Li and Luis Modes},
  journal= {arXiv preprint arXiv:2411.17055},
  year   = {2024}
}

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25 pages

The spherical Hall algebra of $\overline{\operatorname{Spec}(\mathcal{O}_K)}$

Abstract

Keywords

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