Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules
We consider two complexes. The first complex is the twisted de Rham complex of scalar meromorphic differential forms on the projective line, holomorphic on the complement to a finite set of points. The second complex is the chain complex of the Lie algebra of sl₂-valued algebraic functions on the sa...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2019
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210220 |
| 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: | Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules / A. Slinkin, A. Varchenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 9 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862716517075910656 |
|---|---|
| author | Slinkin, A. Varchenko, A. |
| author_facet | Slinkin, A. Varchenko, A. |
| citation_txt | Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules / A. Slinkin, A. Varchenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 9 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider two complexes. The first complex is the twisted de Rham complex of scalar meromorphic differential forms on the projective line, holomorphic on the complement to a finite set of points. The second complex is the chain complex of the Lie algebra of sl₂-valued algebraic functions on the same complement, with coefficients in a tensor product of contragradient Verma modules over the affine Lie algebra sl₂ˆ. In [Schechtman V., Varchenko A., Mosc. Math. J. 17 (2017), 787-802] a construction of a monomorphism of the first complex to the second was suggested, and it was indicated that under this monomorphism, the existence of singular vectors in the Verma modules (the Malikov-Feigin-Fuchs singular vectors) is reflected in the relations between the cohomology classes of the de Rham complex. In this paper, we prove these results.
|
| first_indexed | 2025-12-07T21:24:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-210220 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T21:24:47Z |
| publishDate | 2019 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Slinkin, A. Varchenko, A. 2025-12-04T13:00:07Z 2019 Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules / A. Slinkin, A. Varchenko // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 9 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B56; 17B67; 33C80 arXiv: 1812.09791 https://nasplib.isofts.kiev.ua/handle/123456789/210220 https://doi.org/10.3842/SIGMA.2019.075 We consider two complexes. The first complex is the twisted de Rham complex of scalar meromorphic differential forms on the projective line, holomorphic on the complement to a finite set of points. The second complex is the chain complex of the Lie algebra of sl₂-valued algebraic functions on the same complement, with coefficients in a tensor product of contragradient Verma modules over the affine Lie algebra sl₂ˆ. In [Schechtman V., Varchenko A., Mosc. Math. J. 17 (2017), 787-802] a construction of a monomorphism of the first complex to the second was suggested, and it was indicated that under this monomorphism, the existence of singular vectors in the Verma modules (the Malikov-Feigin-Fuchs singular vectors) is reflected in the relations between the cohomology classes of the de Rham complex. In this paper, we prove these results. The authors thank V. Schechtman for useful discussions. The second author was supported in part by NSF grant DMS-1665239. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules Article published earlier |
| spellingShingle | Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules Slinkin, A. Varchenko, A. |
| title | Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules |
| title_full | Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules |
| title_fullStr | Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules |
| title_full_unstemmed | Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules |
| title_short | Twisted de Rham Complex on Line and Singular Vectors in sl₂ˆ Verma Modules |
| title_sort | twisted de rham complex on line and singular vectors in sl₂ˆ verma modules |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/210220 |
| work_keys_str_mv | AT slinkina twistedderhamcomplexonlineandsingularvectorsinsl2ˆvermamodules AT varchenkoa twistedderhamcomplexonlineandsingularvectorsinsl2ˆvermamodules |