Determinant Formula for Parabolic Verma Modules of Lie Superalgebras

Understand

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.