Abstract
Various constructions for quantum groups have been generalized to \imath -quantum groups. Such a generalization is called an \imath -program. In this paper, we fill one of the parts in the \imath -program. Namely, we provide an equivariant K-theory approach to \imath -quantum groups, which is the Langlands dual picture of that constructed in Bao et al. (Transform. Groups 23 (2018), 329–389), where a geometric realization of \imath -quantum groups is provided by using perverse sheaves. As an application of the main results, we prove Li’s conjecture (Li, Represent. Theory 23 (2019), 1–56) for special cases.
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