Certain Types of Complex Lie Group Action

Abstract

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 tworepresentations , one is usual and the other is the dual, while our interest in this work is focused on some actionson complex Lie group[10] . Let G be a matrix complex group , and is representation of In this study wewill present and analytic the concepts of action of complex group on We recall thedefinition of tensor product of two representations of group and construct the definition of action ofgroup on , then by using the equivalent relation ( ) between and, we get a new action : – The two actionsare forming smooth representation of [ ] [ ] This we have new action which calleddenoted by which acting on( (( ) ) ( ))This is smooth representation of The theoretical Justifications are developed and prove supported bysome concluding remarks and illustrations.