V. Srimathi, Group Representations and Complexity Theory: A Review, Journal of Engineering and Applied Sciences, Volume 7,Issue 6, 2012, Pages 418-420, ISSN 1816-949x, jeasci.2012.418.420, (https://makhillpublications.co/view-article.php?doi=jeasci.2012.418.420) Abstract: Establishing lower bounds for standard algebraic operations is one of the most challenging tasks in Theoretical Computer Science. In this study, researchers discuss lower bounds for matrix multiplication. After a historical review of the progress in this problem. Researchers review a recent development highlighting how the techniques of Group Representation Theory have been applied to give a new approach. Infact, this approach has led to two conjectures whose resolution would achieve the ideal bound for matrix multiplication. Keywords: Theoretical Computer Science;algebraic operations;conjectures;resolution;progress;Group Representation Theory