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Harmonic Analysis and Free Field Realization of the Takiff Supergroup of $\mathrm{GL}(1|1)$
Symmetry, integrability and geometry: methods and applications, Tome 11 (2015) Cet article a éte moissonné depuis la source Math-Net.Ru

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Takiff superalgebras are a family of non semi-simple Lie superalgebras that are believed to give rise to a rich structure of indecomposable representations of associated conformal field theories. We consider the Takiff superalgebra of $\mathfrak{gl}(1\vert 1)$, especially we perform harmonic analysis for the corresponding supergroup. We find that every simple module appears as submodule of an infinite-dimensional indecomposable but reducible module. We lift our results to two free field realizations for the corresponding conformal field theory and construct some modules.
Keywords: logarithmic CFT; Harmonic analysis; free field realization. 
@article{SIGMA_2015_11_a66,
     author = {Andrei Babichenko and Thomas Creutzig},
     title = {Harmonic {Analysis} and {Free} {Field} {Realization} of the {Takiff} {Supergroup} of $\mathrm{GL}(1|1)$},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2015},
     volume = {11},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a66/}
}
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Andrei Babichenko; Thomas Creutzig. Harmonic Analysis and Free Field Realization of the Takiff Supergroup of $\mathrm{GL}(1|1)$. Symmetry, integrability and geometry: methods and applications, Tome 11 (2015). http://geodesic.mathdoc.fr/item/SIGMA_2015_11_a66/

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