Rank ideals and Capelli identities

JOURNAL OF ALGEBRA

卷:273

Article

Protsak, V

关键词: universal enveloping algebra;    rank ideal;    determinantal ideal;    Capelli identity;    reductive dual pair;   

DOI  :  10.1016/S0021-8693(03)00431-9

来源: Elsevier

【 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 x 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. (C) 2004 Elsevier Inc. All rights reserved.

【 授权许可】

Free