Vertex-algebraic structure of principal subspaces of the basic modules for twisted Affine Kac-Moody Lie algebras of type A_2n-1⁽²⁾, D_n⁽²⁾, E₆⁽²⁾

2016/03/08 by Penn, Michael, Sadowski, Christopher
#17B65 #17B69 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1603.02737

Abstract

We obtain a presentation of principal subspaces of basic modules for the twisted affine Kac-Moody Lie algebras of type A_2n-1⁽²⁾, D_n⁽²⁾ and E₆⁽²⁾. Using this presentation, we construct exact sequences among these principal subspaces, and use these exact sequences to obtain recursions satisfied by graded dimensions of the principal subspaces. Solving these recursions, we obtain the graded dimensions of the principal subspaces.

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