Geometric Approach to I-Quantum Group of Affine Type D

In this paper, we study the structures of Schur algebra and Lusztig algebra associated to partial flag varieties of affine type D. We show that there is a subalgebra of Lusztig algebra and the quantum groups arising from this subalgebras via stabilization procedures is a coideal subalgebra of quantum group of affine sl type. We construct monomial and canonical bases of the idempotented quantum algebra and establish the positivity properties of the canonical basis with respect to multiplication and the bilinear pairing.