An Example of Holomorphically Induced Representations of Exponential Solvable Lie Groups

2019 ◽  
pp. 111-120
Author(s):  
Junko Inoue
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups ◽  
Induced Representations

Holomorphically Induced Representations of Solvable Lie Groups

2021 ◽  
pp. 351-399
Author(s):  
Ali Baklouti ◽  
Hidenori Fujiwara ◽  
Jean Ludwig
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups ◽  
Induced Representations

Restricting Representations of Completely Solvable Lie Groups

1990 ◽  
Vol 42 (5) ◽  
pp. 790-824 ◽  
Author(s):  
R. L. Lipsman
Keyword(s):  
Lie Groups ◽  
Dual Problem ◽  
Nilpotent Groups ◽  
Solvable Lie Groups ◽  
Direct Integral ◽  
Induced Representations ◽  
Simply Connected ◽  
Direct Integral Decomposition ◽  
Integral Decomposition ◽  
Restriction Problem

We are concerned here with the problem of describing the direct integral decomposition of a unitary representation obtained by restriction from a larger group. This is the dual problem to the more commonly investigated problem of decomposing induced representations. In this paper we work in the context of completely solvable Lie groups—more general than nilpotent, but less general than exponential solvable. Moreover, the groups involved are simply connected. The restriction problem was considered originally in [2] and in [6] for nilpotent groups.

scholarly journals Harmonically induced representations of solvable Lie groups

1985 ◽  
Vol 62 (1) ◽  
pp. 8-37 ◽  
Author(s):  
Jonathan Rosenberg ◽  
Michèle Vergne
Keyword(s):  
Lie Groups ◽  
Solvable Lie Groups ◽  
Induced Representations

scholarly journals Some groups with T1 primitive ideal spaces

1985 ◽  
Vol 38 (1) ◽  
pp. 55-64 ◽  
Author(s):  
A. L. Carey ◽  
W. Moran
Keyword(s):  
Normal Subgroup ◽  
Lie Groups ◽  
Lie Group ◽  
Locally Compact Group ◽  
Primitive Ideal ◽  
Ideal Space ◽  
Solvable Lie Groups ◽  
Locally Compact ◽  
Simply Connected ◽  
Connected Lie Group

AbstractLet G be a second countable locally compact group possessing a normal subgroup N with G/N abelian. We prove that if G/N is discrete then G has T1 primitive ideal space if and only if the G-quasiorbits in Prim N are closed. This condition on G-quasiorbits arose in Pukanzky's work on connected and simply connected solvable Lie groups where it is equivalent to the condition of Auslander and Moore that G be type R on N (-nilradical). Using an abstract version of Pukanzky's arguments due to Green and Pedersen we establish that if G is a connected and simply connected Lie group then Prim G is T1 whenever G-quasiorbits in [G, G] are closed.

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