Determinant Formula for Parabolic Verma Modules of Lie Superalgebras
Representation Theory
2017-12-12 v1 High Energy Physics - Theory
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.
Keywords
Cite
@article{arxiv.1603.06705,
title = {Determinant Formula for Parabolic Verma Modules of Lie Superalgebras},
author = {Yoshiki Oshima and Masahito Yamazaki},
journal= {arXiv preprint arXiv:1603.06705},
year = {2017}
}
Comments
24 pages