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arXiv · 1603.06705

Determinant Formula for Parabolic Verma Modules of Lie Superalgebras

Yoshiki Oshima·Masahito Yamazaki
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Abstract

We prove a determinant formula for a parabolic Verma module of a Lie superalgebra, previously conjectured by the second author. Our determinant formula generalizes the previous results of Jantzen for a parabolic Verma module of a (non-super) Lie algebra, and of Kac concerning a (non-parabolic) Verma module for a Lie superalgebra. The resulting formula is expected to have a variety of applications in the study of higher-dimensional supersymmetric conformal field theories. We also discuss irreducibility criteria for the Verma module.

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Yoshiki Oshima, Masahito Yamazaki. 2016-03-22. Determinant Formula for Parabolic Verma Modules of Lie Superalgebras. https://doi.org/10.1016/j.jalgebra.2017.11.011

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