Cells in modified $ı$quantum groups of type AIII and related Schur algebras

Abstract

We provide a combinatorial characterization of two-sided cells in modified $ı$quantum groups of type AIII. Our approach is to lift a corresponding description of two-sided cells in $ȷ$-Schur algebras associated to Iwahori--Hecke algebras of type $B$. We further give a combinatorial description of two-sided cells in other two kinds of Schur-type algebras, namely $ı$-Schur algebras and $\tilde{ı}$-Schur algebras.

arXiv commentAdding a few examples and references