in this article, we introduce monomial irreducible representations of the special linear lie algebra $sln$. we will show that this kind of representations have bases for which the action of the chevalley generators of the lie algebra on the basis elements can be given by a simple formula.

In this paper we present a new procedure to obtain unitary and irreducible representations of Lie groups starting from the cotangent bundle of the group (the cotangent group). We discuss some applications of the construction in quantumoptics problems.

Following the construction of the invariant integral and the scalar product for the quantum Euclidean group Eq(2), we obtained the full matrix elements of its unitary irreducible representations from SUq(2) by contraction and then derived the Planscherel measure.

Abstract We begin a systematic study of unitary representations minimal W -algebras. In particular, we classify -algebras and make substantial progress in classification their irreducible highest weight modules. also compute the characters these

Using method of inducing, irreducible unitary representation of Cay-ley–Klein orthogonal groups were constructed. There was proved that Kirilov's method of orbits is relevant for study of the behavior of irre-ducible representations under transitions between Cayley–Klein groups.