Adapted pairs and Weierstrass sections

Abstract

Adapted pairs and Weierstrass sections are central to the invariant theory associated to the action of an algebraic Lie algebra a on a finite dimensional vector space X. In this a need not be a semisimple Lie algebra. Here their general properties are described particularly when a is the canonical truncation of a biparabolic subalgebra of a simple Lie algebra and X is the dual of a.

This short paper is essentially part (see Section 10) of arXiv:1306.0529 "Adapted pairs in type A and regular nilpotent elements" posted on arXiv in June 2013

Cited by in corpus (1)

• Parabolic Adjoint Action, Weierstrass Sections and Components of the Nilfibre in Type $A$