Certain types of complex lie group action

Abstract EN

The main aim in this paper is to look for a novel action with new properties on from the , the Literature are concerned with studying the action of of two representations , one is usual and the other is the dual, while our interest in this work is focused on some actions on complex Lie group[10] .

Let G be a matrix complex group , and is representation of In this study we will present and analytic the concepts of action of complex group on We recall the definition of tensor product of two representations of group and construct the definition of action of group on , then by using the equivalent relation ( ) between and , we get a new action : – The two actions are forming smooth representation of [ ] [ ] This we have new action which called denoted by which acting on ( (( ) ) ( )) This is smooth representation of The theoretical Justifications are developed and prove supported by some concluding remarks and illustrations.