Constructive geometry of arithmetic quotients of symmetric spaces

在项目实施过程中，我们得到了以下成果： 1.非球主级数SL(3,R)Whittaker函数的显式公式。 (2004年发表).2.给定一对算术商(X,Y)，其中X,Y要么是IV型商，要么是复超球的商，当Y是X的约数时，我们将Y的格林电流构造为自守形式。 (2003年发表).3.我们证明了Sp(2,R)的P_J主级数表示中从Siegel-Whittaker函数到Whittaker函数的汇合。 （出版中）4.与爱媛大学的Miki Hirano一起，得到了具有最小K型的GL(3,C)上主级数Whittaker函数的积分和幂级数表达式。该项目仍在进行中。5.Sp(3,R)的P_J主级数表示的显式公式求取项目：内容已完成。我们正在与千叶研究所的 Miki Hirano 和 Taku Ishii 一起准备一篇联合论文。 6.我们在 Komaba 维持了每月一次的自同构型研讨会。

In the period of the project, we got the following results.1.Explicit formula for Whittaker functions of SL(3,R) belonging to non-spherical principal series. (Published in 2004).2.Given a pair of arithmetic quotients (X,Y), where X,Y are either type IV quotients, or quotients of the complex hyperball, and when Y is a divisor of X, we constructed the Green current of Y as an automorphic form. (Published in 2003).3.We proved the confluence from Siegel-Whittaker functions to Whittaker functions for P_J principal series representations of Sp(2,R). (In press).4.Together with Miki Hirano of Ehime University, we obtained the integral and power series expressions of the principal series Whittaker functions on GL(3,C) with minimal K-type. The project is still in progress.5.The project to get explicit formula for P_J principal series representations of Sp(3,R) : The contents are finished. We are preparing a joint paper together with Miki Hirano and Taku Ishii of Chiba Inst. of Technology.6.We maintained the monthly seminar on Automorphic Forms at Komaba.