A variant of the Frobenius reciprocity for restricted representations on nilpotent Lie groups

被引：0

作者：

Baklouti, Ali ^{[1
]}

Fujiwara, Hidenori ^{[2
]}

Ludwig, Jean ^{[3
]}

机构：

[1] Fac Sci Sfax, Dept Math, Sfax 3038, Tunisia

[2] Sch Human Oriented Sci & Engn, Dept Informat & Comp Sci, Lizuka 8208555, Japan

[3] Univ Metz, Fac Sci, Dept Math, F-57045 Metz 01, France

来源：

INFINITE DIMENSIONAL HARMONIC ANALYSIS IV: ON THE INTERPLAY BETWEEN REPRESENTATION THEORY, RANDOM MATRICES, SPECIAL FUNCTIONS, AND PROBABILITY | 2009年

关键词：

nilpotent Lie group; Frobenius reciprocity; coadjoint orbit; polarization; restricted representation; INVARIANT DIFFERENTIAL-OPERATORS; UNITARY REPRESENTATIONS; MULTIPLICITIES; COMMUTATIVITY;

D O I：

10.1142/9789812832825_0002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a nilpotent connected and simply connected Lie. group, K an analytic subgroup of G and pi a unitary and irreducible representation of G. We study in this paper a variant of the Fobenius reciprocity for the restricted representation pi(vertical bar K) of pi on K. It consists in proving that generically, the multiplicity of any isotopic component involved in the central canonical disintegration of pi(vertical bar K) coincides with the dimension of a certain space of generalized tempered distributions which are semi-invariant under the action of a subgroup of K. This problem was considered and partially solved in our previous work (1).

引用

页码：13 / +

页数：3