Conformal Galilei algebras, symmetric polynomials and singular vectors

Abstract

We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras cga(d, C) with d = 1 for any integer value ELEMENT OF N. 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.

Keywords

• Conformal Galilei algebra
• Verma module
• Differential equation of flag type
• Symmetric polynomial