PBW degenerations of Lie superalgebras and their typical representations

29 Oct 2018  ·  Fourier Ghislain, Kus Deniz ·

We introduce the PBW degeneration for basic classical Lie superalgebras and construct for all type I, $\mathfrak{osp}(1,2n)$ 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. read more

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Representation Theory Rings and Algebras