Classification of unitary highest weight representations for non compact real forms

TL;DR

This paper investigates the unitarizability of highest weight representations in Hermitian symmetric spaces, explicitly calculating missing highest weights and constructing their vectors using Jakobsen theorems.

Contribution

It provides a detailed classification of unitary highest weight representations for non-compact real forms, including explicit calculations of missing weights.

Findings

Explicit set of missing highest weights identified

Construction methods for highest weight vectors developed

Enhanced understanding of unitarizability conditions in Hermitian symmetric spaces

Abstract

Using Jakobsen theorems, unitarizability in Hermitian Symmetric Spaces is discussed. The set of all missing highest weights is explicitly calculated and the construction of their corresponding highest weights vectors is studied.