IRREDUCIBLE REPRESENTATIONS OF INFINITE-DIMENSIONAL LIE ALGEBRAS OF CARTAN TYPE

Abstract

In this paper the irreducible representations of infinite-dimensional filtered Lie algebras are studied. The concept of the height of a representation is introduced, and it is proved that the representations of height greater than one of the Lie algebras Wn, Sn, Hn and Kn are induced. The representations of height one of the algebras Wn are also described.