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Algebras and Representation Theory

, Volume 22, Issue 6, pp 1457–1478 | Cite as

Presentations of Principal Subspaces of Higher Level Standard \({A}_{2}^{(2)}\)-Modules

  • Corina CalinescuEmail author
  • Michael Penn
  • Christopher Sadowski
Article
  • 15 Downloads

Abstract

We study the principal subspaces of higher level standard \({A}_{2}^{(2)}\)-modules, extending earlier work in the level one case, by Calinescu, Lepowsky and Milas. We prove natural presentations of principal subspaces and also of certain related spaces. By using these presentations we obtain exact sequences, which yield recursions satisfied by the characters of the principal subspaces and related spaces. We conjecture a formula for a specialized character of the principal subspace, given by the Nahm sum of the inverse of the tadpole Cartan matrix.

Keywords

Twisted affine Lie algebras Twisted vertex-algebra modules Principal subspaces 

Mathematics Subject Classification (2010)

17B69 17B65 05A17 

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Notes

Acknowledgements

We thank the referee for providing us with constructive comments.

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© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Mathematics, New York City College of Technology and the Graduate CenterCity University of New YorkNew YorkUSA
  2. 2.Department of MathematicsRandolph CollegeLynchburgUSA
  3. 3.Department of Mathematics and Computer ScienceUrsinus CollegeCollegevilleUSA

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