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Low Degree Morphisms of E(5, 10)-Generalized Verma Modules

  • Nicoletta Cantarini
  • Fabrizio CaselliEmail author
Article
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Abstract

In this paper we face the study of the representations of the exceptional Lie superalgebra E(5,10). We recall the construction of generalized Verma modules and give a combinatorial description of the restriction to \(\mathfrak {sl}_{5}\) of the Verma module induced by the trivial representation. We use this description to classify morphisms between Verma modules of degree one, two and three proving in these cases a conjecture given by Rudakov (8). A key tool is the notion of dual morphism between Verma modules.

Keywords

Lie superalgebras Verma modules Singular vectors 

Mathematics Subject Classification (2010)

Primary: 17B15 17B25 Secondary 17B65 17B70 

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Dipartimento di MatematicaUniversità di BolognaBolognaItaly

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