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

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...

Повний опис

Збережено в:
Бібліографічні деталі
Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2025
Автор: Kitagawa, Masatoshi
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2025
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/214188
Теги: Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions. Masatoshi Kitagawa. SIGMA 21 (2025), 095, 37 pages

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Опис
Резюме: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 irreducibility of ()ᴳ′-modules in the cases of generalized Verma modules, cohomologically induced modules, and discrete series representations. We treat only discrete decomposable restrictions with certain dominance conditions (quasi-abelian and in the good range). To describe the ()ᴳ′-modules, we give branching laws of cohomologically induced modules using ones of generalized Verma modules when ′ acts on / transitively.
ISSN:1815-0659