Equivariant K-Theory Approach to $\imath$-Quantum Groups

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.