Rank ideals and Capelli identities

✍ Scribed by Victor Protsak

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 232 KB
• Volume: 273
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1016/s0021-8693(03)00431-9

✦ Synopsis

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.