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

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 $C{K}_6$.

arXiv comment19 pages. arXiv admin note: text overlap with arXiv:2103.16374

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• Representations of simple finite Lie conformal superalgebras of type W and S
• Classification of finite irreducible modules over the Lie conformal superalgebra CK6
• Irreducible modules over finite simple Lie conformal superalgebras of type K
• Representations of the Exceptional Lie superalgebra $E(3,6): II. Four series of degenerate modules
• Lie conformal superalgebras and duality of modules over linearly compact Lie superalgebras
• Classification of degenerate Verma modules for E(5,10)
• Classification of finite irreducible conformal modules for $K_4^{\prime }$