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首页> 外文期刊>Annales scientifiques de l'Ecole normale superieure >LOCAL INTEGRABILITY RESULTS IN HARMONIC ANALYSIS ON REDUCTIVE GROUPS IN LARGE POSITIVE CHARACTERISTIC
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LOCAL INTEGRABILITY RESULTS IN HARMONIC ANALYSIS ON REDUCTIVE GROUPS IN LARGE POSITIVE CHARACTERISTIC

机译：大型正特征约简群调和分析的局部可积性结果。

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摘要

Let G be a connected reductive algebraic group over a non-Archimedean local field K, and let g be its Lie algebra. By a theorem of Harish-Chandra, if K has characteristic zero, the Fourier transforms of orbital integrals are represented on the set of regular elements in g (K) by locally constant functions, which, extended by zero to all of g(K), are locally integrable. In this paper, we prove that these functions are in fact specializations of constructible motivic exponential functions. Combining this with the Transfer Principle for integrability of [8], we obtain that Harish-Chandra's theorem holds also when K is a non-Archimedean local field of sufficiently large positive characteristic. Under the hypothesis that mock exponential map exists, this also implies local integrability of Harish-Chandra characters of admissible representations of G(K), where K is an equicharacteristic field of sufficiently large (depending on the root datum of G) characteristic.
机译：令G为非阿基米德局部场K上的连通归约代数群，令g为其李代数。根据Harish-Chandra定理，如果K具有特征零，则轨道积分的傅里叶变换由局部常数函数表示在g（K）中的正则元素集合上，该常数被零扩展到所有g（K） ，在本地可集成。在本文中，我们证明了这些功能实际上是可构造的动力指数函数的专门化。结合[8]的可积性转移原理，我们得到了当K是具有足够大的正特性的非阿希米德局部场时，Harish-Chandra定理也成立。在模拟指数映射存在的假设下，这还意味着G（K）的可容许表示的Harish-Chandra角色的局部可积性，其中K是具有足够大（取决于G根基准）特征的等特征场。

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