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Structure of certain level 2 standard modules for \(A_5^{(2)}\) and the Göllnitz–Gordon identities

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We employ the technique of Lepowsky–Wilson Z-algebras to analyze the structure of certain level 2 standard modules for the affine Lie algebra \(A_5^{(2)}\) that are contained in the tensor product of two inequivalent level 1 standard modules for \(A_5^{(2)}\). As a corollary, we obtain a vertex-operator-theoretic interpretation of the Göllnitz–Gordon identities.

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Acknowledgements

This paper is a part of my Ph.D. thesis [17] completed at Rutgers University. I wish to express my sincere gratitude toward my advisor James Lepowsky for his invaluable guidance and endless support. I thank Robert McRae, Debajyoti Nandi, Matthew Russell, and Andrew Sills for stimulating discussions. I thank the referee for carefully reading the manuscript and for suggesting valuable changes.

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  1. Shashank Kanade

    Present address: Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, T6G 2G1, Canada

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  1. Department of Mathematics, Rutgers, The State University of New Jersey, Piscataway, NJ, 08854, USA

    Shashank Kanade

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  1. Shashank Kanade
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Correspondence to Shashank Kanade.

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Currently supported by a PIMS Post-doctoral Fellowship awarded by The Pacific Institute for the Mathematical Sciences.

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Kanade, S. Structure of certain level 2 standard modules for \(A_5^{(2)}\) and the Göllnitz–Gordon identities. Ramanujan J 45, 873–893 (2018). https://doi.org/10.1007/s11139-016-9875-0

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