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

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.

preprint2015arXivOpen access
Andrei BabichenkoThomas Creutzig
math-phmath.MPhep-th
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Andrei BabichenkoThomas Creutzig

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