Conformal Galilei algebras, symmetric polynomials and singular vectors

摘要

We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras with for any integer value . The homomorphisms are uniquely determined by singular vectors as solutions of certain differential operators of flag type and identified with specific polynomials arising as coefficients in the expansion of a parametric family of symmetric polynomials into power sum symmetric polynomials.