Strongly nilpotent matrices and Gelfand–Zetlin modules

✍ Scribed by Serge Ovsienko

• Publisher: Elsevier Science
• Year: 2003
• Tongue: English
• Weight: 280 KB
• Volume: 365
• Category: Article
• ISSN: 0024-3795
• DOI: 10.1016/s0024-3795(02)00675-4

✦ Synopsis

Let X n be the variety of n × n matrices, which k × k submatrices, formed by the first k rows and columns, are nilpotent for any k = 1, . . . , n. We show, that X n is a complete intersection of dimension (n -1)n/2 and deduce from it, that every character of the Gelfand-Zetlin subalgebra in U(gl n ) extends to an irreducible representation of U(gl n ).