Determinant Formula for Parabolic Verma Modules of Lie Superalgebras

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.

24 pages

References in corpus (4)

• EPFL Lectures on Conformal Field Theory in D>= 3 Dimensions
• TASI Lectures on the Conformal Bootstrap
• Radial expansion for spinning conformal blocks
• Comments on Determinant Formulas for General CFTs

Cited by in corpus (6)

• Weight Shifting Operators and Conformal Blocks
• Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations
• Comments on Determinant Formulas for General CFTs
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• $\mathcal{N}=2$ Supersymmetric Partially Massless Fields and Non-Unitary Superconformal Representations
• Comments on Short Multiplets in Superconformal Algebras