scholarly journals Classification of irreducible modules of certain subalgebras of free boson vertex algebra

2003 ◽  
Vol 270 (1) ◽  
pp. 115-132 ◽  
Author(s):  
Dražen Adamović
Keyword(s):  
Vertex Algebra ◽  
Free Boson ◽  
Irreducible Modules

ADE SUBALGEBRAS OF THE TRIPLET VERTEX ALGEBRA 𝒲(p): D-SERIES

2014 ◽  
Vol 25 (01) ◽  
pp. 1450001 ◽  
Author(s):  
DRAŽEN ADAMOVIĆ ◽  
XIANZU LIN ◽  
ANTUN MILAS
Keyword(s):  
Vertex Algebra ◽  
Constant Term ◽  
Independent Interest ◽  
Irreducible Modules ◽  
Constant Term Identity ◽  
General Method

We are continuing our study of ADE-orbifold subalgebras of the triplet vertex algebra 𝒲(p) initiated in D. Adamović, X. Lin and A. Milas, ADE subalgebras of the triplet vertex algebra 𝒲(p): Am-series, Commun. Contemp. Math.15 (2013), Article ID: 1350028, 1–30. This part deals with the dihedral series. First, subject to a certain constant term identity, we classify all irreducible modules for the vertex algebra [Formula: see text], the ℤ2-orbifold of the singlet vertex algebra [Formula: see text]. Then, we classify irreducible modules and determine Zhu's and C2-algebra for the vertex algebra 𝒲(p)D2. A general method for construction of twisted 𝒲(p)-modules is also introduced. We also discuss classification of twisted [Formula: see text]-modules including the twisted Zhu's algebra [Formula: see text], which is of independent interest. The category of admissible Ψ-twisted [Formula: see text]-modules is expected to be semisimple. We also prove C2-cofiniteness of 𝒲(p)Dm for all m, and give a conjectural list of irreducible 𝒲(p)Dm-modules. Finally, we compute characters of the relevant irreducible modules and describe their modular closure.

scholarly journals Classification of Finite Irreducible Modules over the Lie Conformal Superalgebra CK 6

2012 ◽  
Vol 317 (2) ◽  
pp. 503-546 ◽  
Author(s):  
Carina Boyallian ◽  
Victor G. Kac ◽  
José I. Liberati
Keyword(s):  
Irreducible Modules

scholarly journals Classification of irreducible Harish-Chandra modules over generalized Virasoro algebras

2012 ◽  
Vol 55 (3) ◽  
pp. 697-709 ◽  
Author(s):  
Xiangqian Guo ◽  
Rencai Lu ◽  
Kaiming Zhao
Keyword(s):  
Direct Summand ◽  
Virasoro Algebra ◽  
Additive Subgroup ◽  
One Dimensional ◽  
Finite Dimensional ◽  
Irreducible Modules ◽  
Intermediate Series ◽  
Complex Number Field ◽  
Weight Modules

AbstractLet G be an arbitrary non-zero additive subgroup of the complex number field ℂ, and let Vir[G] be the corresponding generalized Virasoro algebra over ℂ. In this paper we determine all irreducible weight modules with finite-dimensional weight spaces over Vir[G]. The classification strongly depends on the index group G. If G does not have a direct summand isomorphic to ℤ (the integers), then such irreducible modules over Vir[G] are only modules of intermediate series whose weight spaces are all one dimensional. Otherwise, there is one further class of modules that are constructed by using intermediate series modules over a generalized Virasoro subalgebra Vir[G0] of Vir[G] for a direct summand G0 of G with G = G0 ⊕ ℤb, where b ∈ G \ G0. This class of irreducible weight modules do not have corresponding weight modules for the classical Virasoro algebra.

scholarly journals Classification of Irreducible Modules for the Vertex Operator AlgebraM(1)+

1999 ◽  
Vol 216 (1) ◽  
pp. 384-404 ◽  
Author(s):  
Chongying Dong ◽  
Kiyokazu Nagatomo
Keyword(s):  
Vertex Operator ◽  
Irreducible Modules

scholarly journals HIGHEST WEIGHT REPRESENTATIONS AND KAC DETERMINANTS FOR A CLASS OF CONFORMAL GALILEI ALGEBRAS WITH CENTRAL EXTENSION

2012 ◽  
Vol 23 (11) ◽  
pp. 1250118 ◽  
Author(s):  
NARUHIKO AIZAWA ◽  
PHILLIP S. ISAAC ◽  
YUTA KIMURA
Keyword(s):  
Central Extension ◽  
Spatial Dimension ◽  
Verma Modules ◽  
Infinite Dimensional ◽  
Singular Vectors ◽  
Highest Weight ◽  
Irreducible Modules ◽  
Highest Weight Representations ◽  
Quotient Modules

We investigate the representations of a class of conformal Galilei algebras in one spatial dimension with central extension. This is done by explicitly constructing all singular vectors within the Verma modules, proving their completeness and then deducing irreducibility of the associated highest weight quotient modules. A resulting classification of infinite dimensional irreducible modules is presented. It is also shown that a formula for the Kac determinant is deduced from our construction of singular vectors. Thus we prove a conjecture of Dobrev, Doebner and Mrugalla for the case of the Schrödinger algebra.

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