Principal Indecomposable Representations for Restricted Lie Algebras of Cartan Type

Abstract

Let L be any one of W( n, 1), S( n, 1) H( n, 1), and K( n, 1) over an algebraically closed held F of characteristic p > 3. In this paper, we extend the results concerning modular representations of classical Lie algebras and semisimple groups to the case of L and obtain some properties of principal indecomposable modules of u( L) which parallel closely those of classical Lie algebras.