Brownian motions on compact groups of infinite dimension

2003 ◽  
pp. 41-63 ◽  
Author(s):  
Alexander Bendikov ◽  
Laurent Saloff-Coste
Keyword(s):  
Infinite Dimension ◽  
Compact Groups ◽  
Brownian Motions

CENTRAL GAUSSIAN CONVOLUTION SEMIGROUPS ON COMPACT GROUPS: A SURVEY

2003 ◽  
Vol 06 (04) ◽  
pp. 629-659 ◽  
Author(s):  
A. BENDIKOV ◽  
L. SALOFF-COSTE
Keyword(s):  
Compact Groups ◽  
Dimensional Torus ◽  
Orthogonal Groups ◽  
Brownian Motions ◽  
Infinite Products ◽  
Infinite Dimensional ◽  
Convolution Semigroups ◽  
The One ◽  
Infinite Dimensional Torus ◽  
Gaussian Convolution

This is a survey article on Brownian motions on compact connected groups and the associated Gaussian convolution semigroups. The emphasize is on infinite dimensional groups such as the infinite dimensional torus and infinite products of special orthogonal groups. We discuss the existence of Brownian motions having nice properties such as marginales having a continuous density with respect to Haar measure. We relate the existence of these Brownian motions to the algebraic structure of the group. The results we describe reflect the conflicting effects of, on the one hand, the infinite dimensionality and, on the other hand, the compact nature of the underlying group.

Primitivity in representations of polycyclic groups

1980 ◽  
Vol 88 (1) ◽  
pp. 15-31 ◽  
Author(s):  
D. L. Harper
Keyword(s):  
Finite Group ◽  
Irreducible Representation ◽  
Nilpotent Group ◽  
Infinite Dimension ◽  
Finitely Generated ◽  
Polycyclic Groups

In an earlier paper (5) we showed that a finitely generated nilpotent group which is not abelian-by-finite has a primitive irreducible representation of infinite dimension over any non-absolute field. Here we are concerned primarily with the converse question: Suppose that G is a polycyclic-by-finite group with such a representation, then what can be said about G?

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