THE QUEER q-SCHUR SUPERALGEBRA

As a natural generalisation of q-Schur algebras associated with the Hecke algebra H-r,H-R (of the symmetric group), we introduce the queer q-Schur superalgebra associated with the Hecke-Clifford superalgebra H-r,R(c), which, by definition, is the endomorphism algebra of the induced H-r,R(c)-module from certain q-permutation modules over H-r,H-R. 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 q-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 C(v) of complex rational functions.