Determinant formula for parabolic Verma modules of Lie superalgebras

JOURNAL OF ALGEBRA

卷:495

Article

Oshima, Yoshiki¹  Yamazaki, Masahito^2,3 

[1] Osaka Univ, Grad Sch Informat Sci & Technol, Suita, Osaka 5650871, Japan

[2] Univ Tokyo, Kavli IPMU WPI, Kashiwa, Chiba 2778583, Japan

[3] Inst Adv Study, Sch Nat Sci, Princeton, NJ 08540 USA

关键词: Lie superalgebra;    Representation theory;    Verma modules;    Determinant formula;   

DOI  :  10.1016/j.jalgebra.2017.11.011

来源: Elsevier

【 摘 要 】

We prove a determinant formula for a parabolic Verma module of a contragredient finite-dimensional 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. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

Free