Enhanced zeta distributions and its functional equations

Kyo Nishiyama, Bent Ørsted, Akihito Wachi

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Abstract

We consider an "enhanced symmetric space", which is a prehomogeneous vector space. This vector space is intimately related to a double flag variety studied in [1]. On a distinguished open orbit called "enhanced positive cone", we consider a zeta integral with two complex variables, which is analytically continued to meromorphic family of tempered distributions. One of the main results of this paper is to establish a precise formula for the meromorphic continuation which clarifies the location of poles (and may be useful to obtain residues). We also compute the Fourier transform of the zeta distribution and obtain a functional equation with explicit gamma factors.

Original languageEnglish
Article number012081
Book seriesJournal of Physics: Conference Series
Volume1194
Issue1
Number of pages11
ISSN1742-6588
DOIs
Publication statusPublished - 2019
Event32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018 - Prague, Czech Republic
Duration: 9 Jul 201813 Jul 2018

Conference

Conference32nd International Colloquium on Group Theoretical Methods in Physics, ICGTMP 2018
Country/TerritoryCzech Republic
CityPrague
Period09/07/201813/07/2018

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