Harmonic analysis and free field realization of the takiff supergroup of GL(1|1) - Babichenko, Andrei; Creutzig, Thomas (Symmetry Integrability and Geometry-Methods and Applications, 2015)
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(1j1), 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.
CRIS-Team Scopus Importer:2024-06-24
Keywords: Free field realization; Harmonic analysis; Logarithmic CFT