A bound on the degree of singular vectors for the exceptional Lie superalgebra $E(5,10)$

Abstract

We use the language of Lie pseudoalgebras to gain information about the representation theory of the simple infinite-dimensional linearly compact Lie superalgebra of exceptional type $E(5,10)$. This technology allows us to prove that the degree of singular vectors in minimal Verma modules is $\le 14$. A few technical adjustments allow us to refine the bound, proving that the degree must always be $\le 12$ and it is actually, except for a finite number of cases, $\le 10$.

18 pages

References in corpus (3)

• Irreducible Modules over Finite Simple Lie Pseudoalgebras I. Primitive Pseudoalgebras of Type W and S
• Morphisms of Verma modules over exceptional Lie superalgebra E(5,10)
• Irreducible modules over finite simple Lie pseudoalgebras IV. Non-primitive pseudoalgebras

Cited by in corpus (1)

• Classification of degenerate Verma modules for E(5,10)