For around 10 years, the academic research in database has attempted to define a commonly agreed logical modeling for the multidimensional and hierarchical nature of data manipulated with OLAP treatments (called datacube, or cube for short). But only recently has the concept of representation of a cube on a screen, or the optimization of OLAP queries at a logical level, been taken into account in this study. As many others, we believe that these two concepts are essential for the definition of a multidimensional query language. In this article, we propose to consider representations of cubes as first class citizens for query optimisation at the logical level. To reach this goal, we formally define the concept of representation by using the model of complex values [ABI 95]. This allows to have a single model for manipulating both cubes and their representations through typical OLAP operations. These typical operations are studied to propose rewrite rules in order to optimize OLAP querie...