Hidden symmetry and spectral analysis on locally pseudo-Riemannian symmetry spaces

Appears in collection : 2025 - T1 - WS1 - Intertwining operators and geometry

I plan to discuss an application of branching laws in spectral analysis on standard locally symmetric spaces, extending beyond the classical Riemannian setting. Recent advancements have overcome challenges in global analysis with indefinite metrics, thanks to developments in the branching theory of infinite-dimensional representations of reductive groups, which are based on geometries with hidden spherical symmetries. During the lecture, I aim to highlight important, non-technical concepts.

Information about the video

Date of recording 20/01/2025
Date of publication 20/01/2025
Institution IHP
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students, Students
Director(s) Alexandre Duplessis
Format MP4
Venue IHP - Hermite Amphitheater

Citation data

DOI 10.57987/IHP.2025.T1.WS1.001
Cite this video Kobayashi, Toshiyuki (20/01/2025). Hidden symmetry and spectral analysis on locally pseudo-Riemannian symmetry spaces. IHP. Audiovisual resource. DOI: 10.57987/IHP.2025.T1.WS1.001
URL https://dx.doi.org/10.57987/IHP.2025.T1.WS1.001

Domain(s)

Representation Theory

Bibliography

T. Kobayashi : "Discrete decomposability of the restriction of Aq(λ) with respect to reductive subgroups II-micro-local analysis and asymptotic K-support" / Annals of Math., vol. 147 n°3, p. 709-729, 1998.
T. Kobayashi and T. Oshima : "Bounded Multiplicity Theorems for induction and restriction" / Adv. Math., 2013.
T. Kobayashi : "Global analysis by hidden symmetry" / Progress in Mathematics, vol. 323, p. 359-397, 2017 (R. Howe volume).
T. Kobayashi : "Bounded Multiplicity Theorems for Induction and Restriction" / Journal of Lie Theory, vol. 32, p. 197-238, 2022.
F. Kassel and T. Kobayashi : "Invariant differential operators on spherical homogeneous spaces with overgroups" / Journal of Lie Theory, vol. 29, p. 663-754, 2019.
F. Kassel and T. Kobayashi : "Spectral Analysis on Pseudo-Riemannian Locally Symmetric Spaces" / Lecture Notes in Mathematics, vol. 2367, 126 p., 2025.