Spherical Hecke algebras of SL2 over 2-dimensional local fields
Spherical Hecke algebras of SL2 over 2-dimensional local fields
复制标题
二维局部域上 SL2 的球面 Hecke 代数
DOI：
10.1353/ajm.2004.0048
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发表时间：
2004
影响因子：
1.7
通讯作者：
Kyu
中科院分区：
文献类型：
--
作者：
Henry H. Kim;Kyu
本文研究了二维局部场上的球形Hecke代数。为了定义卷积积，我们明确地使用了协集分解。我们还考虑了SL 2环面的球面Hecke代数，并构造了两个球面Hecke代数之间的Satake同构。为了定义Satake同构，我们在由I. Fesenko构造的[inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /]的二维局部域上使用不变测度。
In this paper, we study spherical Hecke algebras of SL 2 over two dimensional local fields. In order to define the convolution product, we make explicit use of coset decompositions. We also consider spherical Hecke algebras of the torus of SL 2 and construct the Satake isomorphism between two spherical Hecke algebras. In order to define the Satake isomorphism, we use the invariant measure on two-dimensional local fields with values in [inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="01i" /] constructed by I. Fesenko.