LAUSR

ABSTRACT We start the study of glider representations in the setting of semisimple Lie algebras. A glider representation is defined for some positively filtered ring FR and here we consider the right bounded algebra filtration FU(????) on the universal enveloping algebra U(????) of some semisimple Lie algebra ???? given by a fixed chain of semisimple Lie subalgebras . Inspired by the classical representation theory, we introduce so called Verma glider representations. Their existence is related to the relations between the root systems of the appearing Lie algebras ????i. In particular, we consider chains of simple Lie algebras of the same type A,B,C and D.