  As a natural generalization quantum Schur algebras associated with the Hecke
algebra of the symmetric group, we introduce the quantum Schur superalgebra of
type Q associated with the Hecke-Clifford superalgebra, which, by definition,
is the endomorphism algebra of the induced module over the Hecke-Clifford
superalgebra from certain permutation modules over the Hecke algebra of the
symmetric group. 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 quantum Schur superalgebra of type Q with
the quantum queer Schur superalgebras investigated in the context of quantum
queer supergroups and then provide a classification of their irreducible
representations over a certain extension of the field of complex rational
functions.
