Free field realization of the twisted Heisenberg–Virasoro algebra at level zero and its applications

Adamović, Dražen; Radobolja, Gordan

doi:10.1016/j.jpaa.2015.02.019

Cited by 20 publications

(33 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The definition of the lattice is slightly changed, but the action of the generators of the Heisenberg-Virasoro algebra is the same as in [2]. Main results of Section 2 of [2] are stated in Proposition 2.1.…”

Section: Results From [2]mentioning

confidence: 99%

“…The study of the twisted Heisenberg-Virasoro algebra at level zero was initiated by Y. Billig [12] motivated by applications to the toroidal Lie algebras. New results on the representation theory were obtained in recent papers [2], [19], [24].…”

Section: Introductionmentioning

confidence: 99%

“…Using free field realization we calculated the fusion rules for non-generic irreducible modules i.e., for those irreducible modules which are not isomorphic to a Verma H-module. In our approach, the screening operator Q introduced in [ (see (2.7) and [2,Theorem 4.3]).…”

Section: Introductionmentioning

confidence: 99%

“…It turned out that the methods from [2] do not provide a free field realization of self-dual modules L H (h, h I ) such that h = c L −2 24 , h I = c L,I . On the other hand, the same paper contains certain results on vanishing of the fusion rules in the category of modules which contains self-dual module L H (h, h I ) as above (see [2,Theorem 5.4(3), Remark 6.5]). In order to understand these fusion rules properties from the vertex-algebraic point of view, one needs to find a bosonic realization of self-dual modules.…”

Section: Introductionmentioning

confidence: 99%

“…Theorem 5.2) becomes a highly reducible H-module Π λ which contains L H (h, h I ) as a submodule. Since Π λ is not a module for the Heisenberg vertex algebra M (1), it is clear that such module could not have appeared in the fusion rules analysis made in [2]. Theorem 5.4] In Section 6 we consider a deformed action on Whittaker Π(0)-modules and obtain a realization of self-dual H-modules L H (h, c L,I ) , h = c L −2 24 [cf.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Self-dual and logarithmic representations of the twisted Heisenberg–Virasoro algebra at level zero

Adamović

Radobolja

2019

Commun. Contemp. Math.

Self Cite

View full text Add to dashboard Cite

This paper is a continuation of [2]. We present certain new applications and generalizations of the free field realization of the twisted Heisenberg-Virasoro algebra H at level zero. We find explicit formulas for singular vectors in certain Verma modules. A free field realization of self-dual modules for H is presented by combining a bosonic construction of Whittaker modules from [7] with a construction of logarithmic modules for vertex algebras. As an application, we prove that there exists a non-split self-extension of irreducible selfdual module which is a logarithmic module of rank two. We construct a large family of logarithmic modules containing different types of highest weight modules as subquotients. We believe that these logarithmic modules are related with projective covers of irreducible modules in a suitable category of H-modules.In Section 2 we recall from [2] a free field realization of H, the definition of vertex algebra Π(0) and its modules Π(p, r). We study an extension of the Heisenberg-Virasoro vertex algebra Π(0) ⊂ Π(0) and present a structure of Π(0)-modules Π(p, r) in Section 3. By using certain relation in Π(0)-modules we recover formula 1.2 in Section 4. Then we consider a deformed action of H on these modules and obtain a family of modules Π(p, r) [cf. Theorem 5.2, Theorem 5.5] with the following properties:• Π(p, r) is a logarithmic H-module with the following action of the element L(0) of the Virasoro algebra:

show abstract

Section: Results From [2]mentioning

confidence: 99%