Fields of invariants for unipotent radicals of parabolic subgroups

TL;DR

This paper investigates the invariants of unipotent radicals in parabolic subgroups of classical groups, providing explicit generators for their fields of invariants under conjugation actions.

Contribution

It explicitly constructs free generators for the fields of invariants for unipotent radicals in parabolic subgroups of classical groups, extending understanding of invariant theory in this context.

Findings

Explicit generators for fields of invariants are provided.

The work applies to classical groups like GL(n), SL(n), O(n), and Sp(2n).

The results facilitate computations in invariant theory for these group actions.

Abstract

The paper is devoted to the problem of finding free generators in the fields of invariants for actions of unipotent groups on affine varieties. We consider the case when the unipotent group is the unipotent radical in an arbitrary parabolic subgroup in the reductive group of classical type GL(n), SL(n), O(n) or Sp(2n). In the explicit form, we present a system of free generators in the field of invariants for the action of the unipotent radical on the reductive group by conjugation.