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Quantum Supergroups III. Twistors

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Abstract

We establish direct connections at several levels between quantum groups and supergroups associated to bar-consistent anisotropic super Cartan datum by constructing an automorphism (called twistor) in the setting of covering quantum groups. The canonical bases of the halves of quantum groups and supergroups are shown to match under the twistor up to powers of \({\sqrt{-1}}\). We further show that the modified quantum group and supergroup are isomorphic over the rational function field adjoined with \({\sqrt{-1}}\), by constructing a twistor on the modified covering quantum group. An equivalence of categories of weight modules for quantum groups and supergroups follows.

Le plus court chemin entre deux vérités dans le domaine réel passe par le domaine complexe.

—Jacques Hadamard

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Authors and Affiliations

  1. Department of Mathematics, University of Virginia, Charlottesville, VA, 22904, USA

    Sean Clark & Weiqiang Wang

  2. Department of Mathematics, University at Buffalo, SUNY, Buffalo, NY, 14260, USA

    Zhaobing Fan & Yiqiang Li

Authors
  1. Sean Clark
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  2. Zhaobing Fan
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  3. Yiqiang Li
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  4. Weiqiang Wang
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Correspondence to Weiqiang Wang.

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Communicated by Y. Kawahigashi

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Clark, S., Fan, Z., Li, Y. et al. Quantum Supergroups III. Twistors. Commun. Math. Phys. 332, 415–436 (2014). https://doi.org/10.1007/s00220-014-2071-4

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  • DOI: https://doi.org/10.1007/s00220-014-2071-4

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