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...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2015
Hauptverfasser: Adamović, D., Lin, X., Milas, A.
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2015
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/146992
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
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.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
_version_ 1862552843888623616
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).
first_indexed 2025-11-25T21:04:11Z
format Article
fulltext
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
publisher Інститут математики НАН України
record_format dspace
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