An upper bound on the degree of singular vectors for $E(1,6)$

TL;DR

This paper establishes an upper bound on the degree of singular vectors in finite Verma modules over the exceptional Lie superalgebra E(1,6), advancing understanding of its representation theory.

Contribution

It proves a previously stated technical result regarding the degree of singular vectors in E(1,6) Verma modules, filling a gap in the literature.

Findings

Proved an upper bound on the degree of singular vectors

Confirmed a conjecture by Boyallian, Kac, and Liberati

Enhanced understanding of E(1,6) representation structure

Abstract

The aim of this work is to prove a technical result, that had been stated by Boyallian, Kac and Liberati \cite{ck6}, on the degree of singular vectors of finite Verma modules over the exceptional Lie superalgebra $E(1,6)$ that is isomorphic to the annihilation superalgebra associated with the conformal superalgebra $CK_{6}$.