$U$-projectors and fields of $U$-invariants

TL;DR

This paper introduces a general method for constructing $U$-projectors, which are algebra homomorphisms into the field of $U$-invariants, and demonstrates their application in identifying generators of invariant fields for reductive group representations.

Contribution

It provides a new, general construction of $U$-projectors and shows how to use them to find generators of invariant fields in reductive group representations.

Findings

Construction of the $U$-projector presented.

Application of $U$-projector to find generators of invariant fields.

Method applicable to representations of reductive groups.

Abstract

We present the general construction of the $U$-projector (the homomorphism of the algebra into its field of $U$-invariants identical on the subalgebra of $U$-invariants). It is shown how to apply $U$-projector to find the systems of free generators of the fields of $U$-invariants for representations of reductive groups.