Weiqiang Wang
This is a survey of some recent progress on quantum symmetric pairs and applications. The topics include quasi K-matrices, $\imath$Schur duality, canonical bases, super Kazhdan-Lusztig theory, $\imath$Hall algebras, current presentations for affine $\imath$quantum groups, and braid group actions.
This paper contains 22 sections, 9 theorems, 34 equations.
Theorem 2.1
BW18aBK19BW18b There exists a unique family of elements $\Upsilon_{\mu} \in \textbf{U}^+_{\mu}$, for $\mu \in {\mathbb N} \mathbb I$, such that $\Upsilon_0 =1$ and $\Upsilon = \sum_{\mu \in {\mathbb N} \mathbb I} \Upsilon_{\mu}$ satisfies the following identity: Moreover, $\Upsilon_{\mu} =0$ unless ${\mu^\theta} = - \mu \in X$. (Recall $\theta = -w_{\bullet} \circ \tau$.)
