Invariants and dualities of a certain parabolic group

TL;DR

This paper proves a conjecture regarding the invariants of a maximal parabolic subgroup of GL(n+1), clarifying the structure of tensor invariants for these groups when n is sufficiently large.

Contribution

It establishes the conjecture from prior work and determines the natural tensor invariants of a specific maximal parabolic subgroup of GL(n+1) for n ≥ r.

Findings

Proof of the conjecture in rom rom prior work.

Determination of natural tensor invariants for the subgroup when n rom r.

Abstract

In this note, I will prove a conjecture in \cite{BYY}, which is related to the invariants of a maximal parabolic subgroup of $\GL_{n+1}$. Consequently, the natural tensor invariants of this typical maximal parabolic subgroup of $\GL_{n+1}$ are determined when $n\geq r$.