Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2025
• ISSN: 1815-0659
• Main Author: Kitagawa, Masatoshi
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2025
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/214188
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions. Masatoshi Kitagawa. SIGMA 21 (2025), 095, 37 pages

In this paper, we study the irreducibility of ()ᴳ′-modules on the spaces of intertwining operators in the branching problem of reductive Lie algebras, and construct a family of finite-dimensional irreducible ()ᴳ′-modules using the Zuckerman derived functors. We provide criteria for the irreducibilit...