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...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2025 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2025
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/214188 |
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| 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| 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.
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| ISSN: | 1815-0659 |