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Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras
We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac-Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Lie algebra and of sl2 (Theorem 3). The formula is derived from a more general but less explicit formula due to Feigin, Fu...
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Інститут математики НАН України
2008
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
| Online Access: | http://dspace.nbuv.gov.ua/handle/123456789/149013 |
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irk-123456789-1490132019-02-20T01:27:04Z Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras Fuchs, D. Wilmarth, C. We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac-Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Lie algebra and of sl2 (Theorem 3). The formula is derived from a more general but less explicit formula due to Feigin, Fuchs and Malikov [Funct. Anal. Appl. 20 (1986), no. 2, 103–113]. In the simpler case of A11 the formula was obtained in [Fuchs D., Funct. Anal. Appl. 23 (1989), no. 2, 154–156]. 2008 Article Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras / D. Fuchs, C. Wilmarth // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 6 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 17B67 http://dspace.nbuv.gov.ua/handle/123456789/149013 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
We prove an explicit formula for a projection of singular vectors in the Verma module over a rank 2 Kac-Moody Lie algebra onto the universal enveloping algebra of the Heisenberg Lie algebra and of sl2 (Theorem 3). The formula is derived from a more general but less explicit formula due to Feigin, Fuchs and Malikov [Funct. Anal. Appl. 20 (1986), no. 2, 103–113]. In the simpler case of A11 the formula was obtained in [Fuchs D., Funct. Anal. Appl. 23 (1989), no. 2, 154–156]. |
| format |
Article |
| author |
Fuchs, D. Wilmarth, C. |
| spellingShingle |
Fuchs, D. Wilmarth, C. Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Fuchs, D. Wilmarth, C. |
| author_sort |
Fuchs, D. |
| title |
Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras |
| title_short |
Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras |
| title_full |
Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras |
| title_fullStr |
Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras |
| title_full_unstemmed |
Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras |
| title_sort |
projections of singular vectors of verma modules over rank 2 kac-moody lie algebras |
| publisher |
Інститут математики НАН України |
| publishDate |
2008 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149013 |
| citation_txt |
Projections of Singular Vectors of Verma Modules over Rank 2 Kac-Moody Lie Algebras / D. Fuchs, C. Wilmarth // Symmetry, Integrability and Geometry: Methods and Applications. — 2008. — Т. 4. — Бібліогр.: 6 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT fuchsd projectionsofsingularvectorsofvermamodulesoverrank2kacmoodyliealgebras AT wilmarthc projectionsofsingularvectorsofvermamodulesoverrank2kacmoodyliealgebras |
| first_indexed |
2023-05-20T17:31:59Z |
| last_indexed |
2023-05-20T17:31:59Z |
| _version_ |
1796153499547860992 |