Invariant Differential Operators on the Schrödinger Model for the Minimal Representation of the Conformal Group

We consider the Schrödinger model of the minimal representation for the conformal group O(2n, 2)(n > 1) which was constructed by Kobayashi-Ørsted [Adv. Math. 2003], and enriched by a series of papers by Kobayashi-Mano [Memoirs of AMS 2011, etc]. We get the joint spectra of the differential operators on the model for generators of the center of the Lie algebra of U(k) × U(n-k) × U(1) for k = 1, ..., n-1. Further, we obtain the generators of the algebra consisting of all invariant differential operators for two compact subgroups I1 × SO(2n-1) × SO(2) and SO(2n) × SO(2) of O(2n, 2)

定曲率空間の曲面の幾何

研究期間:平成11-12年度 ; 研究種目:基盤研究C2 ; 課題番号:11640080原著には既発表論文の別刷を含む