THE BRAUER CHARACTERS AND THE CARTAN MATRIX FOR SL (2 , p)

Document Type : Original Article

Author

Military Technical College, Cairo,Egypt.

Abstract

One way to study the representation theory of a group is to get hold of the simple modules. Finding the multiplicities of these simple modules as composition factors of the principal indecomposable modules (PIM) is a step in this way. These multiplicities are the entries of the Cartan matrix. In this paper, we use the " Orthogonality Relation " (theorem 60.5 ,[12]) of the Brauer characters to get the inverse of the Cartan matrix for the finite Chevalley group of type A1(SL (2,p)) .