Invariants of the coadjoint action on the basic varieties of the unitriangular group

TL;DR

This paper identifies generators of invariant fields under the coadjoint action of the unitriangular group on basic varieties, linking the transcendental degree to Weyl group factorizations, advancing understanding of algebraic invariants.

Contribution

It provides explicit generators for invariant fields and establishes a connection between their transcendental degree and Weyl group factorizations.

Findings

Generators of invariant fields are explicitly described.

Transcendental degree matches the number of factors in Weyl group factorizations.

Results deepen understanding of coadjoint invariants in algebraic groups.

Abstract

We find the generators of the fields of invariants of the coadjoint action of the unitriangular group on the basic varieties and basic cells. It is proved that the transcendental degree of the field of invariants on a basic cell coincides with the number of factors in the special factorization of the associated element of the Weyl group as a product of reflections.