Invariant Krein subspaces, regular irreducibility and integral representations

TL;DR

This paper investigates unitary group representations in Krein spaces, focusing on irreducibility criteria and integral decompositions using Krein subspaces, kernels, and a variant of Choquet's theorem.

Contribution

It introduces new criteria for irreducibility and integral decompositions of representations in Krein spaces, utilizing the theory of Krein subspaces and kernels.

Findings

Established criteria for irreducibility in Krein space representations

Developed a variant of Choquet's theorem for Krein subspaces

Provided methods for integral decompositions of representations

Abstract

We study unitary representations of groups in Krein spaces, irreducibility criteria and integral decompositions. Our main tool is the theory of Krein subspaces and their (reproducing) kernels and a variant of Choquet's theorem.