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

Joint IHP - AIM RTNCG lecture

Abstract: I will discuss symmetry breaking for pairs of real forms of $(GL(n, C), GL(n − 1, C))$. We introduce the concept of "fences for the interlacing pattern," which refines the usual notion of "walls for Weyl chambers." We then present a theorem stating that multiplicity remains constant unless we cross these "fences." This approach is illustrated with examples of both tempered and non-tempered representations, along with a non-vanishing theorem of period integrals for pairs of reductive symmetric spaces.