Positivity of $\imath$-canonical bases

TL;DR

This paper proves positivity properties of the $ extit{i}$-canonical bases in quantum symmetric pairs of type AIII/AIV, enhancing understanding of their structure on modules and tensor products.

Contribution

It establishes new positivity results for $ extit{i}$-canonical bases in quantum symmetric pairs of specific types, expanding the theoretical framework.

Findings

Positivity of $ extit{i}$-canonical bases on simple modules

Positivity on tensor products of modules

Applicability to type AIII/AIV quantum symmetric pairs

Abstract

For the quantum symmetric pair $(\textbf{U}, \textbf{U}^{\imath})$ of type AIII/AIV, we show various positivity properties of the $\imath$-canonical bases on finite-dimensional simple $\textbf{U}$-modules, as well as their tensor product.