Poisson Realization and Quantization of the Geroch Group

TL;DR

This paper identifies the conserved charges of the Geroch group as a quadratic Poisson algebra and proposes their quantization as a Yangian structure, advancing understanding of integrable systems in gravity.

Contribution

It explicitly constructs the Poisson algebra of Geroch charges and suggests a novel quantum algebra framework based on Yangians.

Findings

Conserved charges form a quadratic Poisson algebra.

The algebra structure indicates a Yangian quantum group.

Provides a foundation for quantizing the Geroch group.

Abstract

The conserved nonlocal charges generating the Geroch group with respect to the canonical Poisson structure of the Ernst equation are found. They are shown to build a quadratic Poisson algebra, which suggests to identify the quantum Geroch algebra with Yangian structures.