Simple Virasoro modules induced from codimension one subalgebras of the positive part

Mazorchuk, Volodymyr; Wiesner, Emilie

doi:10.1090/s0002-9939-2014-12098-3

Cited by 41 publications

(21 citation statements)

References 10 publications

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“…At the same time for the last decade, various families of non-weight simple Virasoro modules were studied in [6,9,14,15,18,22,[24][25][26]. These (except the modules in [15,18,24,25]) are basically various versions of Whittaker modules constructed using different tricks. In particular, all the above Whittaker modules and even more were described in a uniform way in [20].…”

Section: Introductionmentioning

confidence: 99%

Tensor product weight modules over the Virasoro algebra

Chen¹,

Guo

Zhao³

2013

Journal of the London Mathematical Society

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Abstract. The tensor product of highest weight modules with intermediate series modules over the Virasoro algebra was discussed by Zhang [Z] in 1997. Since then the irreducibility problem for the tensor products has been open. In this paper, we determine the necessary and sufficient conditions for these tensor products to be simple. From non-simple tensor products, we can get other interesting simple Virasoro modules. We also obtain that any two such tensor products are isomorphic if and only if the corresponding highest weight modules and intermediate series modules are isomorphic respectively. Our method is to develop a "shifting technique" and to widely use Feigin-Fuchs' Theorem on singular vectors of Verma modules over the Virasoro algebra.

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Section: Introductionmentioning

confidence: 99%

Tensor product weight modules over the Virasoro algebra

Chen¹,

Guo

Zhao³

2013

Journal of the London Mathematical Society

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“…They also characterize simple Virasoro modules that are locally finite over a positive part. Motivated by [30], new simple modules for the Virasoro algebra and its extensions have been studied [8,9,26,28,37]. Superconformal algebras have a long history in mathematical physics.…”

Section: Introductionmentioning

confidence: 99%

Simple restricted modules for Neveu-Schwarz algebra

2020

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In this paper, we give a construction of simple modules generalizing both highest weight and Whittaker modules for the Neveu-Schwarz algebra, in the spirit of the work of Mazorchuk and Zhao on simple Virasoro modules. We establish a 1-1 correspondence between simple restricted Neveu-Schwarz modules and simple modules of a family of finite dimensional solvable Lie superalgebras associated to the Neveu-Schwarz algebra. Moreover, for two of these superalgebras all simple modules are classified.

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“…Other work has focused on non-weight L-modules, which attract attention in the past few years, such as Whittaker modules (see, e.g., [13,18,19,21]), C[L 0 ]-free modules, irreducible modules from Weyl modules and a class of non-weight modules including highest-weight-like modules (see, e.g, [1,5,11,14,23,24]). In the present paper, we shall study non-weight Lmodules.…”

Section: Introductionmentioning

confidence: 99%

Irreducible Twisted Heisenberg–Virasoro Modules from Tensor Products

Chen

2019

Results Math

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In this paper, we present a class of non-weight Virasoro modules [14] and [11] respectively. The necessary and sufficient conditions for M V, Ω(λ 0 , α 0 ) ⊗ m i=1 Ω(λ i , α i ) to be irreducible are obtained. Then we determine the necessary and sufficient conditions for two such irreducible Virasoro modules to be isomorphic. At last, we show that the irreducible modules in this class are new.

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Simple Virasoro modules induced from codimension one subalgebras of the positive part

Abstract: Abstract. We construct a new five-parameter family of simple modules over the Virasoro Lie algebra.

Cited by 41 publications

References 10 publications

Tensor product weight modules over the Virasoro algebra

Tensor product weight modules over the Virasoro algebra

Simple restricted modules for Neveu-Schwarz algebra

Irreducible Twisted Heisenberg–Virasoro Modules from Tensor Products

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