Symmetry breaking in Representation Theory
演讲者
Michael Pevzner
时间
2026年05月13日 17:00 至 18:30
地点
A6-101
线上
Zoom 388 528 9728
(BIMSA)
摘要
Restricting a group representation to a subgroup is a central problem in representation theory, concerned with understanding how symmetries decompose when passing to a smaller group. This perspective, commonly referred to as the branching problem, offers a unifying framework
for a range of seemingly disparate phenomena, including fusion rules, Clebsch–Gordan coefficients, Pieri rules for integer partitions, Plancherel-type formulas, the theta correspondence, and, more recently, the Gross–Prasad–Gan conjectures.
Beyond the study of abstract branching laws, a major challenge is the explicit construction of operators that realize symmetry breaking in concrete geometric models of infinite-dimensional representations of real reductive groups. In this talk, we will illustrate these ideas through key examples and outline the guiding principles underlying the emerging theory of symmetry breaking operators.
for a range of seemingly disparate phenomena, including fusion rules, Clebsch–Gordan coefficients, Pieri rules for integer partitions, Plancherel-type formulas, the theta correspondence, and, more recently, the Gross–Prasad–Gan conjectures.
Beyond the study of abstract branching laws, a major challenge is the explicit construction of operators that realize symmetry breaking in concrete geometric models of infinite-dimensional representations of real reductive groups. In this talk, we will illustrate these ideas through key examples and outline the guiding principles underlying the emerging theory of symmetry breaking operators.
演讲者介绍
Michael Pevzner is a professor and the director of the French-Japanese Laboratory of Mathematics and its Interactions. He serves as the managing editor of the Journal of Lie Theory and is the editor of the FJ-LMI Series of Lecture Notes of Mathematics at Springer-Nature. His research focuses on representation theory of Lie groups and Lie algebras, branching problems and symmetry breaking, covariant quantization of symmetric spaces, formality and Kontsevich deformation quantization, and non-commutative harmonic analysis. He is affiliated with both the Graduate School of Mathematical Sciences at The University of Tokyo and the Laboratoire de Mathématiques de Reims.