Mixed-symmetry fields in de Sitter space: a group theoretical glance

TL;DR

This paper classifies unitary irreducible representations of de Sitter space's isometry algebra, linking them to fields, and explores their flat space limits and potential scalar singleton analogs.

Contribution

It rederives characters of all unitary irreducible representations of de Sitter isometry algebra and establishes a dictionary with physical fields, including a novel flat limit approach.

Findings

Characters of all unitary irreducible representations are rederived.

A dictionary between representations and fields on de Sitter space is proposed.

A method for taking the flat limit of these representations is introduced.

Abstract

We rederive the characters of all unitary irreducible representations of the $(d+1)$-dimensional de Sitter spacetime isometry algebra $\mathfrak{so}(1,d+1)$, and propose a dictionary between those representations and massive or (partially) massless fields on de Sitter spacetime. We propose a way of taking the flat limit of representations in (anti-) de Sitter spaces in terms of these characters, and conjecture the spectrum resulting from taking the flat limit of mixed-symmetry fields in de Sitter spacetime. We comment on a possible equivalent of the scalar singleton for the de Sitter (dS) spacetime.