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

最小表示是酉表示的构建块。在此期间，我们建立了不定正交群的极小表示的薛定谔模型，并确定了各向同性锥上L^2-模型上酉逆算子的封闭公式，推广了欧几里德傅里叶变换。文[1]提出了一种新的变形理论。此外，我做了系统的和综合的应用程序的原始理论的可见行动复杂的流形上的多重性自由定理，特别是分支问题的对称对。

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.