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arXiv · 1212.6473

An affine Gindikin-Karpelevich formula

Alexander Braverman·Howard Garland·David Kazhdan·Manish Patnaik
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Abstract

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.

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Alexander Braverman, Howard Garland, David Kazhdan, Manish Patnaik. 2012-12-28. An affine Gindikin-Karpelevich formula. https://arxiv.org/abs/1212.6473

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