Quantum Schur Superalgebras and Kazhdan–lusztig Combinatorics

We introduce the notion of quantum Schur (or q-Schur) superalgebras. These algebras share certain nice properties with q-Schur algebras such as base change property, existence of canonical Z[v, v]-bases, and the duality relation with quantum matrix superalgebra A(m|n). We also construct a cellular Q(υ)-basis and determine its associated cells, called super-cells, in terms of a Robinson–Schensted– Knuth super-correspondence. In this way, we classify all irreducible representations over Q(υ) via super-cell modules.