Minimal polynomials of simple highest weight modules over classical Lie algebras

Abstract

We completely determine the minimal polynomial of an arbitrary simple highest weight module $L(\lambda )$ over a complex classical Lie algebra $\mathfrak{g}\subseteq {\mathfrak{gl}}_N$ relative to its defining module $\pi ={\mathbb{C}}^N$. These results are applied to ordering on primitive ideals and algebraic properties of Howe duality correspondence.

16 pages; January 23, 2008 version

References in corpus (2)

• Minimal polynomials and annihilators of generalized Verma modules of the scalar type
• Transfer of ideals and quantization of small nilpotent orbits