Multiplication formulas and isomorphism theorem of $ı$Schur superalgebras

Abstract

We introduce the notion of $ı$Schur superalgebra, which can be regarded as a type B/C counterpart of the $q$-Schur superalgebra (of type A) formulated as centralizer algebras of certain signed $q$-permutation modules over Hecke algebras. Some multiplication formulas for $ı$Schur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the $ı$Scuhr superalgebras and the $q$-Schur superalgebras of type A, which helps us derive a semisimplicity criteria of the $ı$Schur superalgebras.

v2, 39 pages, minor edit