Rank ideals and Capelli identities

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• 作者：Protsak ; Victor
• 关键词：Universal enveloping algebra ; Rank ideal ; Determinantal ideal ; Capelli identity ; Reductive dual pair
• 刊名：Journal of Algebra
• 出版年：2004
• 期刊代码：69_00218693
• 类别：mt
• 出版时间：March 15, 2004
• 卷：273
• 期：2
• 页码：686-699
• 文件大小：232 K

摘要

We define and study a family of completely prime rank ideals in the universal enveloping algebra U(gl_n). A rank ideal is a noncommutative analogue of a determinantal ideal, the defining ideal for the closure of the set of n×n matrices of fixed rank. We introduce a notion of rank for gl_n-modules and determine the rank of simple highest weight modules and of simple finite-dimensional modules. The main tools are Capelli-type identities and filtered algebra.