Constructive geometry of arithmetic quotients of symmetric spaces

在项目期间，我们得到了以下结果：1。非球面主级数SL（3，R）的Whittaker函数的显式公式。（2004年出版）给定一对等差商（X，Y），其中X，Y或为IV型商，或为复超球的商，且当Y为X的除数时，我们将Y的格林电流构造为自同构形式。（2003年出版）。我们证明了Sp（2，R）的P_J主级数表示从Siegel-Whittaker函数到Whittaker函数的合流性。(印刷中)。4。与爱原大学的Miki Hirano一起，我们得到了最小k型GL（3，C）上的主级数Whittaker函数的积分和幂级数表达式。这个项目仍在进行中。得到Sp（3，R）的P_J主级数表示的显式公式的方案：内容完成。我们正在与千叶工业大学的Miki Hirano和Taku Ishii一起准备一篇联合论文。我们在Komaba维持每月的自同构形式研讨会。

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.