Joint eigenfunctions of the quantum Toda lattice and the quantum cohomology of the flag varieties

我们考虑了户田晶格的量子化。设E是2n维欧几里得空间。设F$是具有光滑快速下降函数的傅里叶积分空间。我们还考虑了F，F '的某个对偶空间。我们看到F'具有D-模结构。我们看到E具有户田格的等能级集的叶理。将Fourier积分分为模空间方向和等水平集方向。我们把Fourier积分对户田格点等水平集的限制称为Radon变换。我们可以定义F '的Radon变换。证明了如果限制微分环的范畴，F'的D-模结构保持不变。作为应用，我们证明了量子户田格的可积性。

We considered the quantization of the Toda lattice. Let E be 2n dimensional Euclid space. Let $F$ be the space of Fourier integrals with smooth rapidly decreasing functions. We also consider a certain dual space of F, F'. We see that F' has D-module structure. We see that E has foliation by iso level set of Toda lattice. The Fourier integrals are divided into direction of moduli space and that of iso level sets. We call the restriction of the Fourier integrals to the iso level set of Toda lattice as Radon transform. We can define Radon transform of F'. We show that if we restrict the category of the ring of differential, the D-module structure of F' is preserved. As application we show that the integrability of the quantum Toda lattice.