This is a survey of some recent progress on quantum symmetric pairs and applications. The
topics include quasi-K-matrices,{Schur duality, canonical bases, super Kazhdan–Lusztig …

We construct quantum supersymmetric pairs (U, U ı) of type AIII and elucidate their
fundamental properties. An ıSchur duality between the ıquantum supergroup U ı and the …

Let g be a complex simple Lie algebra and U q L g the corresponding quantum affine
algebra. We construct a functor F θ between finite-dimensional modules over a quantum …

Recently, Wang and the second author constructed a bar involution and canonical basis for
a quasi-permutation module of the Hecke algebra associated to a type B Weyl group W …

Expanding the classical work of Kazhdan-Lusztig, we construct a bar involution and
canonical bases on the $ q $-Brauer algebra introduced by Wenzl. We define explicit actions …

We introduce the notion of ıSchur superalgebra, which can be regarded as a type B/C
counterpart of the q-Schur superalgebra (of type A) formulated as centralizer algebras of …