scholarly journals Maximal representations of cocompact complex hyperbolic lattices, a uniform approach

2019 ◽  
Vol 6 ◽  
pp. 231-281
Author(s):  
Pierre-Emmanuel Chaput ◽  
Julien Maubon
Keyword(s):  
Uniform Approach ◽  
Maximal Representations ◽  
Hyperbolic Lattices

scholarly journals Maximal representations of uniform complex hyperbolic lattices

2017 ◽  
Vol 185 (2) ◽  
pp. 493-540 ◽  
Author(s):  
Vincent Koziarz ◽  
Julien Maubon
Keyword(s):  
Maximal Representations ◽  
Hyperbolic Lattices

scholarly journals Boundary maps and maximal representations on infinite-dimensional Hermitian symmetric spaces

2021 ◽  
pp. 1-50
Author(s):  
BRUNO DUCHESNE ◽  
JEAN LÉCUREUX ◽  
MARIA BEATRICE POZZETTI
Keyword(s):  
Symmetric Spaces ◽  
Hermitian Symmetric Spaces ◽  
Infinite Dimensional ◽  
Finite Dimensional ◽  
Boundary Map ◽  
Density Assumption ◽  
Maximal Representations ◽  
Tube Type ◽  
Maximal Representation ◽  
Hyperbolic Lattices

Abstract We define a Toledo number for actions of surface groups and complex hyperbolic lattices on infinite-dimensional Hermitian symmetric spaces, which allows us to define maximal representations. When the target is not of tube type, we show that there cannot be Zariski-dense maximal representations, and whenever the existence of a boundary map can be guaranteed, the representation preserves a finite-dimensional totally geodesic subspace on which the action is maximal. In the opposite direction, we construct examples of geometrically dense maximal representation in the infinite-dimensional Hermitian symmetric space of tube type and finite rank. Our approach is based on the study of boundary maps, which we are able to construct in low ranks or under some suitable Zariski density assumption, circumventing the lack of local compactness in the infinite-dimensional setting.

scholarly journals Multiplicative constants and maximal measurable cocycles in bounded cohomology

2021 ◽  
pp. 1-36
Author(s):  
M. MORASCHINI ◽  
A. SAVINI
Keyword(s):  
Bounded Cohomology ◽  
Maximal Representations ◽  
Hyperbolic Lattices ◽  
Cartan Invariant

Abstract Multiplicative constants are a fundamental tool in the study of maximal representations. In this paper, we show how to extend such notion, and the associated framework, to measurable cocycles theory. As an application of this approach, we define and study the Cartan invariant for measurable $\mathrm{PU}(m,1)$ -cocycles of complex hyperbolic lattices.

A uniform approach to static replication

1998 ◽  
Vol 1 (1) ◽  
pp. 73-87 ◽  
Author(s):  
Andrew Chou ◽  
Galin Georgiev
Keyword(s):  
Uniform Approach

scholarly journals Governing information technology (IT) investment: A contingency perspective on organization’s IT investment goals

2021 ◽  
pp. 031289622110095
Author(s):  
Syaiful Ali ◽  
Peter Green ◽  
Alastair Robb ◽  
Adi Masli
Keyword(s):  
Information Technology ◽  
Boards Of Directors ◽  
Contingency Theory ◽  
Jel Classification ◽  
It Investment ◽  
It Investments ◽  
Contingency Perspective ◽  
Uniform Approach ◽  
Business Executives

Using contingency theory, we argue that there is not a uniform approach for companies to govern information technology (IT) investments. Rather, the level of governance over IT investments is contingent upon the organization’s goals for its IT investments. We find that Australian organizations with both operation- and market-focused IT investment goals (i.e. dual-focused IT goals) demonstrate higher IT investment governance (ITIG) levels than those with less focused IT goals. We also document that dual-IT-focused firms that do not implement high levels of ITIG underperform. Our study informs business executives, boards of directors, and other practitioners interested in governance implementations over IT investments. JEL Classification: M1

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