Equivariant K-theory approach to \(\imath\)-quantum groups (Q2165822)

Summary: 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.