Stability of $ı$canonical bases of locally finite type

Abstract

We prove the stability conjecture of $ı$canonical bases, which was raised by Huanchen Bao and Weiqiang Wang in 2016, for all locally finite types. To this end, we characterize the trivial module over the $ı$quantum groups of such type at $q=\infty$. This result can be seen as a very restrictive version of the $ı$crystal base theory for locally finite types.

arXiv comment14 pages