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Conformal Galilei algebras, symmetric polynomials and singular vectors (1612.08891v1)
Published 28 Dec 2016 in math.RT, math-ph, math.AP, math.DG, math.FA, and math.MP
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.