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Gelfand–Kirillov Dimension and Reducibility of Scalar Generalized Verma Modules

摘要：The Gelfand–Kirillov dimension is an invariant which can measure the size of infinitedimensional algebraic structures. In this article, we show that it can also measure the reducibility of scalar generalized Verma modules. In particular, we use it to determine the reducibility of scalar generalized Verma modules associated with maximal parabolic subalgebras in the Hermitian symmetric case.

關鍵詞：
  • dimension  
  • generalized  
  • verma  
  • module  
  • reducibility  
作者：
Zhan; Qiang; BAI; Wei; XIAO
單位：
School; of; Mathematical; Sciences; Soochow; University; Suzhou; 215006; P.R.China; College; of; Mathematics; and; statistics; Shenzhen; Key; Laboratory; of; Advanced; Machine; Learning; Applications; Shenzhen; University; Shenzhen; 518060; P.R.China
刊名：
數(shù)學學報

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期刊名稱：數(shù)學學報

數(shù)學學報緊跟學術前沿，緊貼讀者，國內(nèi)刊號為：11-2038/O1。堅持指導性與實用性相結合的原則，創(chuàng)辦于1936年，雜志在全國同類期刊中發(fā)行數(shù)量名列前茅。