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arXiv · 2601.01610

Hecke algebra of $\mathrm{GL}_n$ over a 2-dimensional local field

Xuecai Ma
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Abstract

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.

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Xuecai Ma. 2026-01-04. Hecke algebra of $\mathrm{GL}_n$ over a 2-dimensional local field. https://arxiv.org/abs/2601.01610

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