Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities
We consider AD-type orbifolds of the triplet vertex algebras W(p) extending the well-known c=1 orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras A(W(p)Am) and A(W(p)Dm), where Am and Dm are cyclic and dihedral groups, respectively. A combinatorial algorithm for clas...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2015 |
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Інститут математики НАН України
2015
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/146992 |
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| Zitieren: | Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities / D. Adamović, X. Lin, A. Milas // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 15 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862552843888623616 |
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| author | Adamović, D. Lin, X. Milas, A. |
| author_facet | Adamović, D. Lin, X. Milas, A. |
| citation_txt | Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities / D. Adamović, X. Lin, A. Milas // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 15 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We consider AD-type orbifolds of the triplet vertex algebras W(p) extending the well-known c=1 orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras A(W(p)Am) and A(W(p)Dm), where Am and Dm are cyclic and dihedral groups, respectively. A combinatorial algorithm for classification of irreducible W(p)Γ-modules is developed, which relies on a family of constant term identities and properties of certain polynomials based on constant terms. All these properties can be checked for small values of m and p with a computer software. As a result, we argue that if certain constant term properties hold, the irreducible modules constructed in [Commun. Contemp. Math. 15 (2013), 1350028, 30 pages; Internat. J. Math. 25 (2014), 1450001, 34 pages] provide a complete list of irreducible W(p)Am and W(p)Dm-modules. This paper is a continuation of our previous work on the ADE subalgebras of the triplet vertex algebra W(p).
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| first_indexed | 2025-11-25T21:04:11Z |
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| id | nasplib_isofts_kiev_ua-123456789-146992 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T21:04:11Z |
| publishDate | 2015 |
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| spelling | Adamović, D. Lin, X. Milas, A. 2019-02-12T18:04:23Z 2019-02-12T18:04:23Z 2015 Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities / D. Adamović, X. Lin, A. Milas // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 15 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 17B69 DOI:10.3842/SIGMA.2015.019 https://nasplib.isofts.kiev.ua/handle/123456789/146992 We consider AD-type orbifolds of the triplet vertex algebras W(p) extending the well-known c=1 orbifolds of lattice vertex algebras. We study the structure of Zhu's algebras A(W(p)Am) and A(W(p)Dm), where Am and Dm are cyclic and dihedral groups, respectively. A combinatorial algorithm for classification of irreducible W(p)Γ-modules is developed, which relies on a family of constant term identities and properties of certain polynomials based on constant terms. All these properties can be checked for small values of m and p with a computer software. As a result, we argue that if certain constant term properties hold, the irreducible modules constructed in [Commun. Contemp. Math. 15 (2013), 1350028, 30 pages; Internat. J. Math. 25 (2014), 1450001, 34 pages] provide a complete list of irreducible W(p)Am and W(p)Dm-modules. This paper is a continuation of our previous work on the ADE subalgebras of the triplet vertex algebra W(p). This paper is a contribution to the Special Issue on New Directions in Lie Theory. The full collection is
 available at http://www.emis.de/journals/SIGMA/LieTheory2014.html.
 We would like to thank the referees for their valuable comments. D.A. is partially supported by
 the Croatian Science Foundation under the project 2634. X.L. is partially supported by National
 Natural Science Foundation for young (no. 11401098). A.M. is partially supported by a Simons
 Foundation grant. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities Article published earlier |
| spellingShingle | Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities Adamović, D. Lin, X. Milas, A. |
| title | Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities |
| title_full | Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities |
| title_fullStr | Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities |
| title_full_unstemmed | Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities |
| title_short | Vertex Algebras W(p)Am and W(p)Dm and Constant Term Identities |
| title_sort | vertex algebras w(p)am and w(p)dm and constant term identities |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146992 |
| work_keys_str_mv | AT adamovicd vertexalgebraswpamandwpdmandconstanttermidentities AT linx vertexalgebraswpamandwpdmandconstanttermidentities AT milasa vertexalgebraswpamandwpdmandconstanttermidentities |