Abstract
We introduce a new quantized enveloping superalgebra \({\mathfrak {U}}_q{\mathfrak {p}}_n\) attached to the Lie superalgebra \({\mathfrak {p}}_n\) of type P. The superalgebra \({\mathfrak {U}}_q{\mathfrak {p}}_n\) is a quantization of a Lie bisuperalgebra structure on \({\mathfrak {p}}_n\), and we study some of its basic properties. We also introduce the periplectic q-Brauer algebra and prove that it is the centralizer of the \({\mathfrak {U}}_q{\mathfrak {p}}_n\)-module structure on \({\mathbb {C}}(n|n)^{\otimes l}\). We end by proposing a definition for a new periplectic q-Schur superalgebra.
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Acknowledgements
The second named author is partly supported by the Simons Collaboration Grant 358245. He also would like to thank the Max Planck Institute in Bonn (where part of this work was completed) for the excellent working conditions. The third named author gratefully acknowledges the financial support of the Natural Sciences and Engineering Research Council of Canada provided via the Discovery Grant Program. We thank Patrick Conner, Robert Muth, and Vidas Regelskis for help with certain computations in the preliminary stages of the present paper. We also thank Nicholas Davidson and Jonathan Kujawa for useful discussions. Finally, we are grateful to the referees for valuable suggestions.
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Ahmed, S., Grantcharov, D. & Guay, N. Quantized enveloping superalgebra of type P. Lett Math Phys 111, 84 (2021). https://doi.org/10.1007/s11005-021-01424-y
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DOI: https://doi.org/10.1007/s11005-021-01424-y