On Semisimplicity of Jantzen Middles for the Periplectic Lie Superalgebra

被引：0
|
作者：
Chen, Chih-Whi [1 ]
机构：
[1] Natl Cent Univ, Dept Math, Taoyuan 320317, Taiwan
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2022年
关键词：
KAZHDAN-LUSZTIG CONJECTURE; ENVELOPING ALGEBRA; PRIMITIVE-IDEALS; REPRESENTATIONS; CLASSIFICATION; FUNCTORS;
D O I：
10.1093/imrn/rnac01
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We prove that an integral block of the category O of the periplectic Lie superalgebra contains a non-semisimple Jantzen middle if and only if it contains a simple module of atypical highest weight. As a consequence, every atypical integral block of O does not admit a Kazhdan-Lusztig theory in the sense of Cline, Parshall, and Scott.
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