2025/12/17 by Lu, Ming, Zhao, Zhuoyi
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)
paper · doi:10.48550/arxiv.2512.15322
A quantum symmetric pair consists of a quantum group \widetildeU and its coideal subalgebra \widetildeU^\imath. The Hall algebra constructions of \widetildeU and \widetildeU^\imath are given by Bridgeland and Lu--Wang, respectively. In this paper, we construct a Hall algebra framework for the coideal subalgebra structure of \widetildeU^\imath in \widetildeU, and for the quantum symmetric pair (\widetildeU,\widetildeU^\imath). As an application, we prove that the natural embedding \imath:\widetildeU^\imath→ \widetildeU, and the coproduct Δ:\widetildeU^\imath→ \widetildeU^\imath⊗ \widetildeU preserve the integral forms of \widetildeU^\imath and \widetildeU, which are used to construct the dual canonical bases.