Multiplication formulas and isomorphism theorem of ıSchur 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 semisimplicity criteria of the ı Schur superalgebras.