THE Q-q-SCHUR SUPERALGEBRA
نویسنده
چکیده
As a natural generalisation of q-Schur algebras associated with the Hecke algebra Hr,R (of the symmetric group), we introduce the Q-q-Schur superalgebra associated with the Hecke-Clifford superalgebra H r,R, which, by definition, is the endomorphism algebra of the induced H r,R-module from certain q-permutation modules over Hr,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 Q-q-Schur superalgebras 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 C(v) of complex rational functions. We dedicate the paper to the memory of Professor James A. Green
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