Effective constructions in plethysms and Weintraub's conjecture

TL;DR

This paper provides a concise proof of Weintraub's conjecture by explicitly constructing highest weight vectors within symmetric powers of even exterior powers, advancing understanding in representation theory.

Contribution

It offers a new, explicit construction method for highest weight vectors that simplifies the proof of Weintraub's conjecture.

Findings

Successful explicit construction of highest weight vectors

Short proof of Weintraub's conjecture

Enhanced understanding of plethysm structures

Abstract

We give a short proof of Weintraub's conjecture by constructing explicit highest weight vectors in the symmetric power of an even exterior power.