In the present paper, we start the systematic explicit construction of invariant differential
operators by giving explicit description of one of the main ingredients—the cuspidal …

The present paper contains two interrelated developments. First, the basic elements of the
theory of lowest weight modules, in particular, of Verma modules, over certain non …

We give a group-theoretic interpretation of the AdS/CFT correspondence as relation of
representation equivalence between representations of the conformal group describing the …

We give a review of some group-theoretical results related to nonrelativistic holography. Our
main playgrounds are the Schrödinger equation and the Schrödinger algebra. We first recall …

A bstract In the present paper we continue the project of systematic construction of invariant
differential operators for non-compact semisimple Lie groups. Our starting points is the class …

For a given Lie superalgebra, two ways of constructing color superalgebras are presented.
One of them is based on the color superalgebraic nature of the Clifford algebras. The …

The ℓ-conformal Galilei algebra, denoted by ${\mathfrak {g}} _ {\ell}(d), $ is a non-
semisimple Lie algebra specified by a pair of parameters (d, ℓ). The algebra is regarded as a …

We give explicit formulae for singular vectors of Verma modules over U q (G), where G is any
complex simple Lie algebra. The vectors we present correspond exhaustively to a class of …

We construct representations pi r of the quantum algebra U q (sl (n)) labelled by n-1 complex
numbers ri and acting in the space of formal power series of n (n-1)/2 non-commuting …

We investigate the representations of the exotic conformal Galilei algebra. This is done by
explicitly constructing all singular vectors within the Verma modules, and then deducing …