Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Restriction to Subgroups

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2022
• Main Author: Nakahama, Ryosuke
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2022
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/211635
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Computation of Weighted Bergman Inner Products on Bounded Symmetric Domains and Restriction to Subgroups. Ryosuke Nakahama. SIGMA 18 (2022), 033, 105 pages

Let (𝐺, 𝐺₁) be a symmetric pair of holomorphic type, and we consider a pair of Hermitian symmetric spaces 𝐷₁ = 𝐺₁/𝛫₁ ⊂ 𝐷 = 𝐺/𝛫, realized as bounded symmetric domains in complex vector spaces p⁺₁ ⊂ p⁺ respectively. Then the universal covering group 𝐺˜ of 𝐺 acts unitarily on the weighted Bergman space...