The queer q-Schur superalgebra

As a natural generalisation of-Schur algebras associated with the Hecke algebra (of the symmetric group), we introduce the queer-Schur superalgebra associated with the Hecke-Clifford superalgebra , which, by definition, is the endomorphism algebra of the induced-module from certain-permutation modules over . We will describe certain integral bases for these superalgebras in terms of matrices and will establish the base-change property for them. We will also identify the queer-Schur superalgebras with the quantum queer Schur superalgebras investigated in the context of quantum queer supergroups and provide a constructible classification of their simple polynomial representations over a certain extension of the field of complex rational functions.