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Reducibility of generalized Verma modules for Hermitian symmetric pairs

Authors:	Zhanqiang Bai Wei Xiao

Institution:	1. School of Mathematical Sciences, Soochow University, Suzhou 215006, P. R. China;2. College of Mathematics and Statistics, Shenzhen Key Laboratory of Advanced Machine Learning and Applications, Shenzhen University, Shenzhen, 518060, Guangdong, P. R. China;1. University of Coimbra, CMUC, Department of Mathematics, 3001-501 Coimbra, Portugal;2. Dipartimento di Matematica “Federigo Enriques”, Università degli Studi di Milano, Via Saldini 50, 20133 Milano, Italy;1. Faculty of Science, University of Toyama, 3190 Gofuku, Toyama-shi 930-8555, Japan;2. Statistics and Mathematics Unit, Indian Statistical Institute, 203 B.T. Road, Kolkata 700 108, India

Abstract:	In this article, we give some practical criteria to determine the reducibility of generalized Verma modules (induced from finite-dimensional modules) in the Hermitian symmetric case. Our criteria are given by the information of the corresponding highest weights of the finite-dimensional modules and relatively easy to verify. This article is inspired by earlier work of Kubo about Jantzen's criterion.

Keywords:	Generalized Verma module Jantzen's criterion Reducibility Hermitian symmetric pair
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