An affine Gindikin-Karpelevich formula
An affine Gindikin-Karpelevich formula
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仿射 Gindikin-Karpelevich 公式
DOI：
10.1090/conm/610/12193
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发表时间：
2012
期刊：
影响因子：
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通讯作者：
M. Patnaik
中科院分区：
文献类型：
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作者：
A. Braverman;H. Garland;D. Kazhdan;M. Patnaik
本文给出了局部非阿基米德域K上仿射Kac-Moody群的有限性结果的初等证明。我们的结果意味着那些早期证明的布雷弗曼-Kazhdan，布雷弗曼-芬克尔伯格-Kazhdan和Gaussent-Rousseau使用代数几何或卡茨-穆迪版本的Bruhat-Tits建设。
上面的有限性结果允许我们用一个仿射形式的Gindikin-Karpelevich公式来表示，当K具有正特征时，它与Braverman-Finkelberg-Kazhdan讨论的公式相一致。我们推导出这个公式从仿射版本的麦克唐纳公式的球函数，这将证明在随后的出版物。
In this paper we give an elementary proof of certain finiteness results about affine Kac-Moody groups over a local non-archimedian field K. Our results imply those proven earlier by Braverman-Kazhdan, Braverman-Finkelberg-Kazhdan and Gaussent-Rousseau using either algebraic geometry or a Kac-Moody version of the Bruhat-Tits building.
The above finiteness results allow one to formulate an affine version of the Gindikin-Karpelevich formula, which coincides with the one discussed by Braverman-Finkelberg-Kazhdan in the case when K has positive characteristic. We deduce this formula from an affine version of the Macdonald formula for the spherical function, which will be proved in a subsequent publication.