Higher-Order Differential Operators on a Lie Group and Quantization

TL;DR

This paper introduces higher-order polarization within the Group Approach to Quantization, providing a method to ensure irreducible representations of Lie groups when traditional techniques fail.

Contribution

It presents a novel concept of higher-order polarization that enhances the quantization process for Lie groups, especially in challenging cases.

Findings

Higher-order polarization guarantees irreducibility of representations.

Applicable when Kostant-Kirilov and Borel-Weyl-Bott methods fail.

Strengthens the Group Approach to Quantization.

Abstract

This talk is devoted mainly to the concept of higher-order polarization on a group, which is introduced in the framework of a Group Approach to Quantization, as a powerful tool to guarantee the irreducibility of quantizations and/or representations of Lie groups in those anomalous cases where the Kostant-Kirilov co-adjoint method or the Borel-Weyl-Bott representation algorithm do not succeed.