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arXiv · 1411.1072

Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1)

Andrei Babichenko·Thomas Creutzig
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Abstract

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 gl(1|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.

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Andrei Babichenko, Thomas Creutzig. 2014-11-04. Harmonic Analysis and Free Field Realization of the Takiff Supergroup of GL(1|1). https://doi.org/10.3842/sigma.2015.067

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