Equivariant K-Theory Approach to -Quantum Groups

  • Zhaobing Fan

    Harbin Engineering University, China
  • Haitao Ma

    Harbin Engineering University, China
  • Husileng Xiao

    Harbin Engineering University, China
Equivariant K-Theory Approach to $\imath$-Quantum Groups cover

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Abstract

Various constructions for quantum groups have been generalized to -quantum groups. Such a generalization is called an -program. In this paper, we fill one of the parts in the -program. Namely, we provide an equivariant K-theory approach to -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 -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.

Cite this article

Zhaobing Fan, Haitao Ma, Husileng Xiao, Equivariant K-Theory Approach to -Quantum Groups. Publ. Res. Inst. Math. Sci. 58 (2022), no. 3, pp. 635–668

DOI 10.4171/PRIMS/58-3-6