Analysis of minimal representations and branching laws of infinite-dimensional representations

最小表示是酉表示的基石之一。经典的例子是Weil表示，自20世纪90年代以来，许多专家对代数进行了深入的研究。与此相反，我提出了另一种几何方法来最小表示，我们可以期待一个富有成效的理论，全球分析的最大对称性。它包括L^2模型上的酉逆算子理论，该理论推广了具有G. Mano（[Memoirs of AMS，1000，（2011）]），[Compositio Math.2012]中的傅立叶变换的变形理论，满足与G. Mano，希尔格特和Moellers在[Ramanujan J. 2011]中，以及在Jordan代数框架中的Schroodinger/Fock模型的推广等。

Minimal representations are one of building blocks of unitary representations. Classic examples are the Weil representation, and intensive algebraic studies have been made since 1990s by many experts. In contrast, I proposed yet another geometric approach to minimal representations, by which we could expect a fruitful theory on global analysis by maximal symmetries. It includes a theory of unitary inversion operator on the L^2-model that generalizes the Euclidean Fourier transform with G. Mano ([Memoirs of AMS, 1000, (2011)]), a deformation theory of the Fourier transform in [Compositio Math. 2012], a theory of new "special functions" satisfying a certain ODE of order four with G. Mano, Hilgert, and Moellers in [Ramanujan J. 2011], and a generalization of the Schroodinger/Fock model in the framework of the Jordan algebra among others.