The de Sitter group and its presence at the late-time boundary

Abstract

Our main goal here is to provide an introduction on some of the well established properties of the representation theory of SO(d+1,1), for those considering to think on physical problems set in de Sitter space in terms of these representations. With this purpose we review two intertwining maps, the map G that is used in constructing a well defined inner product for the complementary series representations and the map Q that is involved in constructing composite representations. We give explicit examples from the late-time boundary of de Sitter on the practical use of the complementary series inner product and in building a tensor product representation from unitary principal series irreducible representations.

submitted to Proceedings of Science, Corfu Summer Institute 2021 "School and Workshops on Elementary Particle Physics and Gravity" under the workshop on "Quantum Features in a de Sitter Universe"

References in corpus (2)

• Analyticity and Unitarity for Cosmological Correlators
• Tensors and Spinors in de Sitter Space

Cited by in corpus (4)

• (Non-)unitarity of strictly and partially massless fermions on de Sitter space
• (Non-)unitarity of strictly and partially massless fermions on de Sitter space II: an explanation based on the group-theoretic properties of the spin-3/2 and spin-5/2 eigenmodes
• Hidden Conformal Symmetry of the Discrete Series Scalars in dS${}_2$
• Unconventional conformal invariance of maximal depth partially massless fields on $d{S}_4$ and its relation to complex partially massless SUSY