Restrictions of irreducible unitary representations of nilpotent Lie groups to lattices

被引：4

作者：

Bekka, MB ^{[1
]}

Driutti, P ^{[1
]}

机构：

[1] Univ Metz, Dept Math, F-57045 Metz 01, France

来源：

JOURNAL OF FUNCTIONAL ANALYSIS | 1999年 / 168卷 / 02期

关键词：

restriction; representation; lattice; polarization; rational;

D O I：

10.1006/jfan.1999.3473

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 real Lie group and let Gamma be a lattice in G. We characterize the irreducible representations of G that remain irreducible when restricted to Gamma. (C) 1999 Academic Press.

引用

页码：514 / 528

页数：15

共 12 条

[1]

[Anonymous], 1962, USPEHI MAT NAUK

[2] QUP and Paley-Wiener properties of unimodular, especially nilpotent, Lie groups [J].

Arnal, D ;

Ludwig, J .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1997, 125 (04) :1071-1080

[3] CHARACTER FORMULAS AND SPECTRA OF COMPACT NILMANIFOLDS [J].

CORWIN, L ;

GREENLEAF, FP .

JOURNAL OF FUNCTIONAL ANALYSIS, 1976, 21 (02) :123-154

[4] INDUCED REPRESENTATIONS OF DISCRETE GROUPS [J].

CORWIN, L .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 47 (02) :279-287

[5]

COWLING M, 1991, J REINE ANGEW MATH, V420, P85

[6] INTEGRAL DECOMPOSITION OF REPRESENTATIONS OF NILPOTENT LIE GROUPS [J].

FELIX, R .

MANUSCRIPTA MATHEMATICA, 1979, 27 (03) :279-290

[7] REPRESENTATIONS OF DISCRETE, FINITELY GENERATED, TORSION-FREE, NILPOTENT GROUPS [J].

HOWE, RE .

PACIFIC JOURNAL OF MATHEMATICS, 1977, 73 (02) :281-305

[8]

Kirillov, 1962, RUSS MATH SURV, V17, P53, DOI [DOI 10.1070/RM1962V017N04ABEH004118, 10.1070/RM1962v017n0]

[9] INDUCED REPRESENTATIONS OF LOCALLY COMPACT GROUPS-I [J].

MACKEY, GW .

ANNALS OF MATHEMATICS, 1952, 55 (01) :101-139

[10]

Mackey GW., 1951, Amer. J. Math, V73, P576, DOI [10.2307/2372309, DOI 10.2307/2372309]

← 1 2 →