Invariant Differential Operators on the Schr\"{o}dinger Model for the Minimal Representation of the Conformal Group
Vol. 18 (2011), No. 3, Page 355--395.
Kowata, Atsutaka; Moriwaki, Masayasu
Invariant Differential Operators on the Schr\"{o}dinger Model for the Minimal Representation of the Conformal Group
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Abstract:
We consider the Schr\"{o}dinger model of the minimal representation for the conformal group O(2n,2)(n>1) which was constructed by Kobayashi-\O rsted [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).
Mathematics Subject Classification (2010): Primary 22E45; Secondary 47F05.
Received: 2011-08-10
