J. Segar

Intertwining operators for ℓ-conformal Galilei algebras and hierarchy of invariant equations

l-Conformal Galilei algebra, denoted by g{l}{d}, is a non-semisimple Lie algebra specified by a pair of parameters (d,l). The algebra is regarded as a nonrelativistic analogue of the conformal algebra. We derive hierarchies of partial differential equations which have invariance of the group generated by g{l}{d} with central extension as kinematical symmetry. This is done by developing a representation theory such as Verma modules, singular vectors of g{l}{d} and vector field representations for d = 1, 2.

Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras

The conformal Galilei algebra (CGA) is a non-semisimple Lie algebra labelled by two parameters

Basic hypergeometric functions and covariant spaces for even-dimensional representations of Uq[osp(1/2)]

d

Z2×Z2 generalizations of 𝒩=2 super Schrödinger algebras and their representations

and

Universal T-matrix, representations of OSpq(1/2) and little Q-Jacobi polynomials

\ell

Generalized boson algebra and its entangled bipartite coherent states

. The aim of the present work is to investigate the lowest weight representations of CGA with

Aspects of infinite dimensional ℓ-super Galilean conformal algebra

d = 1

Representations of conformal Galilei algebra with integer spin and an application

for any integer value of

Representations of ℓ-conformai Galilei algebra and hierarchy of invariant equation

\ell

Noncommutative Complex Manifolds via Coherent States of Quantum Groups and Supergroups

. First we focus on the reducibility of the Verma modules. We give a formula for the Shapovalov determinant and it follows that the Verma module is irreducible if