Invariants of the adjoint action in the nilradical of a parabolic subalgebra of types Bn, Cn, Dn

TL;DR

This paper investigates algebraic invariants under the adjoint action within the nilradical of certain parabolic subalgebras, introducing new concepts and establishing independence and degree estimates for these invariants.

Contribution

It introduces the expanded base concept for positive roots and constructs algebraically independent invariants for each root, advancing understanding of invariants in Lie algebra theory.

Findings

Constructed invariants for each root of the expanded base.

Proved the algebraic independence of these invariants.

Provided an estimate for the transcendence degree of the invariant field.

Abstract

We study invariants of the adjoint action of the unipotent group in the nilradical of a parabolic subalgebra of types Bn, Cn, Dn. We introduce the notion of expanded base in the set of positive roots and construct an invariant for every root of the expanded base. We prove that these invariants are algebraically independent. We also give an estimate of the transcendence degree of the field of invariants.