Branching Laws for Representations of a Non-Compact Orthogonal Group

Explore the intricacies of branching laws for representations of a non-compact orthogonal group in this AWM-AMS Noether Lecture delivered by Birgit Speh from Cornell University at the Joint Mathematics Meetings 2020 in Denver, CO. Delve into a comprehensive overview of the topic, starting with an introduction and background, before progressing to the Notice Theorem and its original article. Examine the connections to quantum field theory and classical results, focusing on multiplicities in the context of noncompact and special orthogonal groups. Investigate finite-dimensional and irreducible representations, multiplicity definitions, parameters, and height concepts. Learn about patching rules and their implications for multiplicities, particularly in cases of same signature. Conclude with remarks and the presentation of an appreciation plaque in this 49-minute lecture that bridges advanced mathematical concepts with their practical applications.

Introduction
Background
Notice Theorem
Original Article
Quantum Field Theory
Classical Results
Multiplicities
Noncompact Orthogonal Group
Special Orthogonal Group
Finite dimensional representations
Irreducible representations
Multiplicity definition
Parameters
Height
Patching Rules
Multiplicity
Same Signature
Remarks
Appreciation Plaque