Hecke algebra of $\mathrm{GL}_n$ over a 2-dimensional local field
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866918271791398912 |
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| author | Ma, Xuecai |
| author_facet | Ma, Xuecai |
| contents | Using the $\mathbb{R}((X))$-measure, we define and study certain $\mathbb{C}((X))$-valued functions on $\mathrm{GL}_n(F)$ for $F$ a two-dimensional local field. In particular, we define a convolution product on such suitable functions, which leads us to define the Hecke algebra of $\mathrm{GL}_n(F)$. We then define the measurable $\mathbb{C}((X))$-representations of $\mathrm{GL}_n(F)$, and prove that function space is a candidate for such representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_01610 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Hecke algebra of $\mathrm{GL}_n$ over a 2-dimensional local field Ma, Xuecai Number Theory Using the $\mathbb{R}((X))$-measure, we define and study certain $\mathbb{C}((X))$-valued functions on $\mathrm{GL}_n(F)$ for $F$ a two-dimensional local field. In particular, we define a convolution product on such suitable functions, which leads us to define the Hecke algebra of $\mathrm{GL}_n(F)$. We then define the measurable $\mathbb{C}((X))$-representations of $\mathrm{GL}_n(F)$, and prove that function space is a candidate for such representations. |
| title | Hecke algebra of $\mathrm{GL}_n$ over a 2-dimensional local field |
| topic | Number Theory |
| url | https://arxiv.org/abs/2601.01610 |