Equivariant K-theory approach to $ı$-quantum groups

Abstract

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

28 pages