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 |
|---|---|
| Дата: | 2025 |
| ISSN: | 1815-0659 |
| 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| _version_ | 1862550771125452800 |
|---|---|
| author | Kitagawa, Masatoshi |
| author_facet | Kitagawa, Masatoshi |
| citation_txt | Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions. Masatoshi Kitagawa. SIGMA 21 (2025), 095, 37 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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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| first_indexed | 2026-03-21T11:47:05Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-214188 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:47:05Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Kitagawa, Masatoshi 2026-02-20T07:58:45Z 2025 Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions. Masatoshi Kitagawa. SIGMA 21 (2025), 095, 37 pages 1815-0659 2020 Mathematics Subject Classification: 22E46; 22E47 arXiv:2410.17125 https://nasplib.isofts.kiev.ua/handle/123456789/214188 https://doi.org/10.3842/SIGMA.2025.095 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. This work is based on a part of my Ph.D. Thesis under the supervision of Professor Toshiyuki Kobayashi. I am deeply grateful to him for his continuous support, invaluable advice, and constant encouragement. I thank the anonymous referees for valuable comments that improved the exposition and clarified the results. This work was supported by JSPS KAKENHI Grant Number JP23K12963. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions Article published earlier |
| spellingShingle | Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions Kitagawa, Masatoshi |
| title | Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions |
| title_full | Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions |
| title_fullStr | Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions |
| title_full_unstemmed | Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions |
| title_short | Construction of Irreducible ()ᴳ′-Modules and Discretely Decomposable Restrictions |
| title_sort | construction of irreducible ()ᴳ′-modules and discretely decomposable restrictions |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214188 |
| work_keys_str_mv | AT kitagawamasatoshi constructionofirreduciblegmodulesanddiscretelydecomposablerestrictions |