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A SERRE PRESENTATION FOR THE ıQUANTUM GROUPS

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Abstract

Let (U, Uı) be a quasi-split quantum symmetric pair of arbitrary Kac–Moody type, where “quasi-split” means the corresponding Satake diagram contains no black node. We give a presentation of the ıquantum group Uı with explicit ıSerre relations. The verification of new ıSerre relations is reduced to some new q-binomial identities. Consequently, Uı is shown to admit a bar involution under suitable conditions on the parameters.

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Authors and Affiliations

  1. Department of Mathematics, Southwest Jiaotong University, Chengdu, 610031, P. R. China

    XINHONG CHEN

  2. Department of Mathematics, Sichuan University, Chengdu, 610064, P. R. China

    MING LU

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

    WEIQIANG WANG

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  1. XINHONG CHEN
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  2. MING LU
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  3. WEIQIANG WANG
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Correspondence to MING LU.

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Xinhong Chen is supported by NSFC grant 11601441 and the Fundamental Research Funds for the Central Universities grant 2682016CX109.

Weiqiang Wang is supported by NSF grant DMS-1702254.

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CHEN, X., LU, M. & WANG, W. A SERRE PRESENTATION FOR THE ıQUANTUM GROUPS. Transformation Groups 26, 827–857 (2021). https://doi.org/10.1007/s00031-020-09581-5

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  • DOI: https://doi.org/10.1007/s00031-020-09581-5

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