Massless Representations in Conformal Space and Their de Sitter (dS) Restrictions. The Split-Octonionic Fabric of Inflationary Field Dynamics

The monograph develops a self-contained, mathematically rigorous framework for massless representations of the conformal group U(2,2) and their restriction to the de Sitter group Sp(2,2). It systematically constructs ladder (massless) representations, computes invariant bilinear forms and Casimir operators, and provides explicit constructions of vertex operators and two-point functions for low-helicity fields. The monograph employs a novel Clifford-split-octonion approach, embedding 8-component Majorana spinors within an alternative composition algebra, which allows for fully explicit algebraic, spinorial, and geometric constructions. The text bridges foundational representation theory, explicit computational methods, and physical applications in quantum field theory and cosmology. While targeted at researchers in mathematical physics, quantum cosmology, and quantum field theory, the exposition is pedagogically structured to guide advanced graduate students through subtle algebraic and representation-theoretic ideas, making complex constructions accessible without sacrificing rigor.