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

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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.

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Acknowledgements

We thank the referee for providing us with constructive comments.

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Authors and Affiliations

  1. Department of Mathematics, New York City College of Technology and the Graduate Center, City University of New York, New York, NY, 10016, USA

    Corina Calinescu

  2. Department of Mathematics, Randolph College, Lynchburg, VA, 24503, USA

    Michael Penn

  3. Department of Mathematics and Computer Science, Ursinus College, Collegeville, PA, 19426, USA

    Christopher Sadowski

Authors
  1. Corina Calinescu
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  2. Michael Penn
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  3. Christopher Sadowski
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Corresponding author

Correspondence to Corina Calinescu.

Additional information

Presented by: Peter Littelmann

C.C was partially supported by the Simons Foundation Collaboration Grant for Mathematicians, and by PSC-CUNY Research Awards.

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Calinescu, C., Penn, M. & Sadowski, C. Presentations of Principal Subspaces of Higher Level Standard \({A}_{2}^{(2)}\)-Modules. Algebr Represent Theor 22, 1457–1478 (2019). https://doi.org/10.1007/s10468-018-9828-y

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