Analysis of restrictions of unitary representations of a nilpotent Lie group |
| |
Authors: | Ali Baklouti Hidenori Fujiwara |
| |
Affiliation: | a Faculté des sciences de Sfax, département de mathématiques, route de Soukra, 3038 Sfax, Tunisia b Université de Kinki, faculté de technologie à Kyushu, 820-8555 Iizuka, Japan c Département de mathématiques, faculté des sciences, université de Metz, Ile du Saulcy, 57045 Metz cedex 01, France |
| |
Abstract: | Let G be a connected simply connected nilpotent Lie group, K an analytic subgroup of G and π an irreducible unitary representation of G. Let DπK(G) be the algebra of differential operators keeping invariant the space of C∞ vectors of π and commuting with the action of K on that space. In this paper, we assume that the restriction of π to K has finite multiplicities and we show that DπK(G) is isomorphic to a subalgebra of the field of rational K-invariant functions on the co-adjoint orbit Ω(π) associated to π, and for some particular cases, that DπK(G) is even isomorphic to the algebra of polynomial K-invariant functions on Ω(π). We prove also the Frobenius reciprocity for some restricted classes of nilpotent Lie groups, especially in the cases where K is normal or abelian. |
| |
Keywords: | 22E27 |
本文献已被 ScienceDirect 等数据库收录! |
|