Conformal Galilei algebras, symmetric polynomials and singular vectors

Abstract

We classify and explicitly describe homomorphisms of Verma modules for conformal Galilei algebras ${\mathfrak{cga}}_{\ell }(d,\mathbb{C})$ with $d=1$ for any integer value $\ell \in \mathbb{N}$. 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.

References in corpus (3)

• Galilean Conformal Algebras and AdS/CFT
• Algebraic analysis on scalar generalized Verma modules of Heisenberg parabolic type I.: $A_n$-series
• Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras

Cited by in corpus (5)

• Transposed Poisson structures on Galilean and solvable Lie algebras
• Polynomial representations of classical Lie algebras and flag varieties
• Irreducible representations of simple Lie algebras by differential operators
• Self-adjoint extension for Maxwell-Chern-Simons model in long wavelength limit
• Tensor products and intertwining operators between two uniserial representations of the Galilean Lie algebra $\mathfrak{sl}(2)⋉{\mathfrak{h}}_n$