PBW Degenerations of Lie Superalgebras and their Typical Representations

G. Fourier; D. Kus

doi:10.5802/jolt.1173

G. Fourier; D. Kus

Journal of Lie Theory, Volume 31 (2021) no. 2, pp. 313-334

Abstract

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.

arXiv Zbl

DOI: 10.5802/jolt.1173

Classification: 17A70, 17B10, 52B20
Keywords: PBW degeneration, Lie superalgebra, monomial bases

@article{JOLT_2021_31_2_a1,
     author = {G. Fourier and D. Kus},
     title = {PBW {Degenerations} of {Lie} {Superalgebras} and their {Typical} {Representations}},
     journal = {Journal of Lie Theory},
     pages = {313--334},
     year = {2021},
     volume = {31},
     number = {2},
     doi = {10.5802/jolt.1173},
     zbl = {1482.17026},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1173/}
}

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G. Fourier; D. Kus. PBW Degenerations of Lie Superalgebras and their Typical Representations. Journal of Lie Theory, Volume 31 (2021) no. 2, pp. 313-334. doi: 10.5802/jolt.1173

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