Equivariant K-theory approach to $\imath$-quantum groups

Zhaobing Fan; Haitao Ma; Husileng Xiao

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arXiv · 1911.00851

Equivariant K-theory approach to $\imath$-quantum groups

Zhaobing Fan·Haitao Ma·Husileng Xiao

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Abstract

Various constructions for quantum groups have been generalized to $\imath$-quantum groups. Such generalization is called $\imath$-program. In this paper, we fill one of parts in the $\imath$-program. Namely, we provide an equivariant K-theory approach to $\imath$-quantum groups associated to the Satake diagram in \eqref{eq1}, which is the Langlands dual picture of that constructed in \cite{BKLW14}, where a geometric realization of the $\imath$-quantum group is provided by using perverse sheaves. As an application of the main results, we prove Li's conjecture \cite{L18} for the special cases with the satake diagram in \eqref{eq1}.

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BibTeX RIS

Zhaobing Fan, Haitao Ma, Husileng Xiao. 2019-11-03. Equivariant K-theory approach to $\imath$-quantum groups. https://arxiv.org/abs/1911.00851

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