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A Classical q-Hypergeometric Approach to the \(A_2^{(2)}\) Standard Modules

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Book cover Analytic Number Theory, Modular Forms and q-Hypergeometric Series (ALLADI60 2016)

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Abstract

This is a written expansion of the talk delivered by the author at the International Conference on Number Theory in Honor of Krishna Alladi for his 60th Birthday, held at the University of Florida, March 17–21, 2016. Here, we derive Bailey pairs that give rise to Rogers–Ramanujan type identities, the product sides of which are known to be the principally specialized characters of the \(A_2^{(2)}\) standard modules \((\ell - 2i+2)\varLambda _0 + (i-1)\varLambda _1\) for any level \(\ell \), and \(i=1, 2\).

Dedicated to Krishna Alladi on the occasion of his 60th birthday

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Acknowledgements

The author thanks Jim Lepowsky for assistance with the exposition and the referee for carefully reading the manuscript and providing a number of useful suggestions for improvement.

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Authors and Affiliations

  1. Georgia Southern University, Statesboro, Georgia

    Andrew V. Sills

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  1. Andrew V. Sills
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Correspondence to Andrew V. Sills .

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Editors and Affiliations

  1. Department of Mathematics, Pennsylvania State University, State College, Pennsylvania, USA

    George E. Andrews

  2. Department of Mathematics, University of Florida, Gainesville, Florida, USA

    Frank Garvan

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Sills, A.V. (2017). A Classical q-Hypergeometric Approach to the \(A_2^{(2)}\) Standard Modules. In: Andrews, G., Garvan, F. (eds) Analytic Number Theory, Modular Forms and q-Hypergeometric Series. ALLADI60 2016. Springer Proceedings in Mathematics & Statistics, vol 221. Springer, Cham. https://doi.org/10.1007/978-3-319-68376-8_39

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