## Arkady Onishchik - Transitive irreducible Lie superalgebras of vector fields

cm:10456 - Communications in Mathematics, December 14, 2022, Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik) - https://doi.org/10.46298/cm.10456
Transitive irreducible Lie superalgebras of vector fields

Authors: Arkady Onishchik

Let $\mathfrak{d}$ be the Lie superalgebra of superderivations of the sheaf of sections of the exterior algebra of the homogeneous vector bundle $E$ over the flag variety $G/P$, where $G$ is a simple finite-dimensional complex Lie group and $P$ its parabolic subgroup. Then, $\mathfrak{d}$ is transitive and irreducible whenever $E$ is defined by an irreducible $P$-module $V$ such that the highest weight of $V^*$ is dominant. Moreover, $\mathfrak{d}$ is simple; it is isomorphic to the Lie superalgebra of vector fields on the superpoint, i.e., on a $0|n$-dimensional supervariety.

Volume: Volume 30 (2022), Issue 3 (Special issue: in memory of Arkady Onishchik)
Published on: December 14, 2022
Accepted on: December 11, 2022
Submitted on: December 11, 2022
Keywords: Mathematics - Representation Theory,32C11, 17B20

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