报告题目：Affine flag varieties and quantum symmetric pairs
报告摘要：The quantum groups of finite and affine type A admit geometric realizations in terms of partial flag varieties of finite and affine type A. Recently, the quantum group associated to partial flag varieties of finite type B/C is shown to be a coideal subalgebra of the quantum group of finite type A. In this talk, I will introduce the structures of Schur algebras and Lusztig algebras associated to partial flag varieties of affine type C. We show that the quantum groups arising from Lusztig algebras and Schur algebras via stabilization procedures are (idempotented) coideal subalgebras of quantum groups of affine sl_n and gl_n types, respectively. In this way, we provide geometric realizations of eight quantum symmetric pairs of affine types. We construct monomial and canonical bases of all these quantum (Schur, Lusztig, and coideal) algebras. For the idempotented coideal algebras of affine sl_n type, we establish the positivity properties of the canonical basis with respect to multiplication, comultiplication and a bilinear pairing. In particular, we obtain a new and geometric construction of the idempotented quantum affine gl_n and its canonical basis. This is a joint work with C. Lai, Y. Li, L. Luo and W. Wang.