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Colloquium
Seminar information archive ～01/17｜Next seminar｜Future seminars 01/18～
| Organizer(s) | ASUKE Taro, TERADA Itaru, HASEGAWA Ryu, MIYAMOTO Yasuhito (chair) |
|---|---|
| URL | https://www.ms.u-tokyo.ac.jp/seminar/colloquium_e/index_e.html |
2024/11/15
15:30-16:30 Room #大講義室 (Graduate School of Math. Sci. Bldg.)
Michael Pevzner (University of Reims / CNRS / The University of Tokyo)
Symmetry breaking for branching problems (ENGLISH)
https://forms.gle/DcsJVYS4fvMLfPEM8
Michael Pevzner (University of Reims / CNRS / The University of Tokyo)
Symmetry breaking for branching problems (ENGLISH)
[ Abstract ]
Restricting a group representation to its subgroups is a fundamental issue in Representation Theory. This process involves exploring how large symmetries can be broken down into smaller symmetries. Known as the branching problem, it provides a unifying framework for various seemingly disparate topics, including fusion rules, Clebsch-Gordan coefficients, Pieri rules for integral partitions, Plancherel-type formulas, Theta correspondence, and more recently, the Gross-Prasad-Gan conjectures.
Beyond analyzing abstract branching rules, constructing explicit operators that implement this symmetry breaking in concrete geometric models of infinite-dimensional representations of real reductive groups is a compelling and challenging problem. This field, located at the intersection of global analysis, Lie Theory, the geometry of homogeneous spaces, and algebraic representation theory, has attracted significant attention over the past decade. We will illustrate these concepts with key examples and provide an overview of the guiding principles that are shaping the emerging theory of symmetry breaking operators, along with original ideas related to holographic transforms and the associated generating operators.
[ Reference URL ]Restricting a group representation to its subgroups is a fundamental issue in Representation Theory. This process involves exploring how large symmetries can be broken down into smaller symmetries. Known as the branching problem, it provides a unifying framework for various seemingly disparate topics, including fusion rules, Clebsch-Gordan coefficients, Pieri rules for integral partitions, Plancherel-type formulas, Theta correspondence, and more recently, the Gross-Prasad-Gan conjectures.
Beyond analyzing abstract branching rules, constructing explicit operators that implement this symmetry breaking in concrete geometric models of infinite-dimensional representations of real reductive groups is a compelling and challenging problem. This field, located at the intersection of global analysis, Lie Theory, the geometry of homogeneous spaces, and algebraic representation theory, has attracted significant attention over the past decade. We will illustrate these concepts with key examples and provide an overview of the guiding principles that are shaping the emerging theory of symmetry breaking operators, along with original ideas related to holographic transforms and the associated generating operators.
https://forms.gle/DcsJVYS4fvMLfPEM8
