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arXiv · 1612.08891

Conformal Galilei algebras, symmetric polynomials and singular vectors

Libor Křižka·Petr Somberg
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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.

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Libor Křižka, Petr Somberg. 2016-12-28. Conformal Galilei algebras, symmetric polynomials and singular vectors. https://doi.org/10.1007/s11005-017-0997-0

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