On the representations of the full matrix semigroup on homogeneous polynomials

Abstract

This paper is the successor of [ 11. In the closing theorem there we determined the composition factors of w” for a regular I [ 1, 6.11. Here we are going to describe the structure of WA in the singular case. The second theme of this paper is the criterion for distributivity of the M -modules WCd’ Since the necessary conditions for that established in [ 1: 8.51 limit d to’d <p( p + 1) we just have to sort out the latter case. This will be done in the third section of this paper. For the convenience of the reader we recall some notation, terms, and definitions used in [ 11.