Multiplication formulas and isomorphism theorem of ıSchur superalgebras

We introduce the notion of ıSchur 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 ıSchur superalgebra are obtained to construct their canonical bases. Furthermore, we established an isomorphism theorem between the ıScuhr superalgebras and the q-Schur superalgebras of type A, which helps us derive semisimplicity criteria of the ıSchur superalgebras.