Appears in collection : 2025 - T1 - Representation theory and noncommutative geometry

Standard subspaces in a Hilbert space are closely related to the modular and Tomita--Takesaki theory theory, two cornerstones in Algebraic Quantum Field Theory (AQFT). In this talk we start with a short overview of the theory of standard subspaces and the connection to the Tomita--Takesaki theory. We will then discuss Euler elements and causal symmetric spaces and then connect those two subjects via representation theory, analytic continuation to the crown and then limit processes to realize standard subspaces in spaces of distribution vectors.