Modules de plus haut poids unitarisables sur la super-algèbre de Virasoro N=2 tordue

Iohara, Kenji

doi:10.5802/aif.2367

Cited by 3 publications

(1 citation statement)

References 9 publications

(11 reference statements)

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“…Both physicists and mathematicians have obtained several interesting examples and classification results for these Lie superalgebras. Examples include the N = 1 and N = 2 super Virasoro algebras [BFD86], [FQS85], [GKO86], [Io10,Io08], superconformal current algebras [KaTo], and affine Lie superalgebras [JaKa], [JaZh88].…”

Section: Introductionmentioning

confidence: 99%

Positive definite superfunctions and unitary representations of lie supergroups

Neeb

Salmasian

2013

Transformation Groups

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Abstract. For a broad class of Fréchet-Lie supergroups G, we prove that there exists a correspondence between positive definite smooth (resp., analytic) superfunctions on G and matrix coefficients of smooth (resp., analytic) unitary representations of the Harish-Chandra pair (G, g) associated to G.As an application, we prove that a smooth positive definite superfunction on G is analytic if and only if it restricts to an analytic function on the underlying manifold of G.When the underlying manifold of G is 1-connected we obtain a necessary and sufficient condition for a linear functional on the universal enveloping algebra U (g C ) to correspond to a matrix coefficient of a unitary representation of (G, g).The class of Lie supergroups for which the aforementioned results hold is characterised by a condition on the convergence of the Trotter product formula. This condition is strictly weaker than assuming that the underlying Lie group of G is a locally exponential Fréchet-Lie group. In particular, our results apply to examples of interest in representation theory such as mapping supergroups and diffeomorphism supergroups.

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Section: Introductionmentioning

confidence: 99%

Positive definite superfunctions and unitary representations of lie supergroups

Neeb

Salmasian

2013

Transformation Groups

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Unitarizable Highest Weight Modules of the N = 2 Super Virasoro Algebras: Untwisted Sectors

Iohara¹

2010

Lett Math Phys

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Irreducible modules over N = 2 superconformal algebras arising from algebraic D-modules

Chen,

Dai,

Liu

et al. 2024

Journal of Mathematical Physics

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In this paper, we introduce a family of functors denoted as Fb, which act on algebraic D-modules and produce modules over N = 2 superconformal algebras. We demonstrate that these functors preserve irreducibility for all values of b, except for explicitly outlined cases. Moreover, we establish the necessary and sufficient conditions for determining the natural isomorphism between two such functors. Our constructed functors recover specific irreducible modules over N = 2 superconformal algebras, including intermediate series and U(h)-free modules. Additionally, we show that our constructed functors yield several new irreducible modules for N = 2 superconformal algebras.

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Modules de plus haut poids unitarisables sur la super-algèbre de Virasoro N=2 tordue

Cited by 3 publications

References 9 publications

Positive definite superfunctions and unitary representations of lie supergroups

Positive definite superfunctions and unitary representations of lie supergroups

Unitarizable Highest Weight Modules of the N = 2 Super Virasoro Algebras: Untwisted Sectors

Irreducible modules over N = 2 superconformal algebras arising from algebraic D-modules

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