2022-01-21T05:58:01Zhttps://repository.dl.itc.u-tokyo.ac.jp/oaioai:repository.dl.itc.u-tokyo.ac.jp:000400392021-03-02T02:38:48ZInvariant Differential Operators on the Schrödinger Model for the Minimal Representation of the Conformal GroupKowata, Atsutaka92486Moriwaki, Masayasu92487415Schrödinger modelminimal representationconformal groupunitary groupspherical harmonicsinvariant differential operatorsWe 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).departmental bulletin paperGraduate School of Mathematical Sciences, The University of Tokyo2011-12-16application/pdfJournal of mathematical sciences, the University of Tokyo318355395AA1102165313405705https://repository.dl.itc.u-tokyo.ac.jp/record/40039/files/jms180304.pdfeng