Transformation groups for geometric structures, global geometric analysis, and theory of branching laws of infinite dimensional representations

最小表示是单位表示的组成部分。在此期间，我们建立了不定正交群最小表示的薛定谔模型，并确定了各向同性锥体上L^2模型上的幺正反演算子的封闭公式，推广了欧几里得傅里叶变换。在b[1]中引入了一种新的变形理论。在此基础上，我将原有的复数流形可见作用理论系统地综合应用于无多重性定理，特别是对称对的分支问题。

Minimal representations are building blocks of unitary representations. During this period, we established the Schrodinger model of minimal representations of the indefinite orthogonal group, and determined a closed formula of the unitary inversion operator on the L^2-model on the isotropic cones, that generalizes the Euclidean Fourier transform. A new deformation theory was introduced in [1]. Further, I made systematic and synthetic applications of the original theory of visible actions on complex manifolds to multiplicity-free theorems, in particular, branching problems to symmetric pairs.