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Journal of Lie Theory 31 (2021), No. 2, 313--334
Copyright Heldermann Verlag 2021

PBW Degenerations of Lie Superalgebras and their Typical Representations

Ghislain Fourier
RWTH Aachen, 52062 Aachen, Germany

Deniz Kus
Ruhr-Universitšt Bochum, 44780 Bochum, Germany

We introduce the PBW degeneration for basic classical Lie superalgebras and construct for all type I, osp(1,2n) and exceptional Lie superalgebras new monomial bases. These bases are parametrized by lattice points in convex lattice polytopes, sharing useful properties such as the integer decomposition property. This paper is the first step towards extending the framework of PBW degenerations to the Lie superalgebra setting.

Keywords: PBW degeneration, Lie superalgebra, monomial bases.

MSC: 17A70, 17B10, 52B20.

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