Abstract
We introduce the notion of quantum Schur (or q -Schur) superalgebras. These algebras share certain nice properties with q -Schur algebras such as the base change property, the existence of canonical Z [ v , v − 1 ] -bases, the duality relation with Manin’s quantum matrix superalgebra A ( m | n ) , and the bridging role between quantum enveloping superalgebras of g l ( m | n ) and the Hecke algebras of type A . We also construct a cellular Q ( υ ) -basis and determine its associated cells, called supercells, in terms of a Robinson–Schensted–Knuth supercorrespondence. In this way, we classify all irreducible representations over Q ( υ ) via supercell modules.
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