In this paper, we embed the integral form of the quantum supergroup U_v(gl_(m|n)) to the product of a family of integral quantum Schur super algebras. We show that the image of the embedding is a free Z[v, v^(-1)]-mod...In this paper, we embed the integral form of the quantum supergroup U_v(gl_(m|n)) to the product of a family of integral quantum Schur super algebras. We show that the image of the embedding is a free Z[v, v^(-1)]-module by finding the basis explicitly and calculating the fundamental multiplication formulas of these bases. Unlike the non-super case, the fundamental multiplication formula, which is the key step, is more complicated since we have to deal with the case of multiplying the odd root vectors. As a consequence, via the base change, we realize the quantum supergroup at roots of unity as a subalgebra of the product of quantum Schur superalgebras. Thus, we find a new basis of quantum supergroups at odd roots of unity which comes from quantum Schur superalgebras.展开更多
基金supported by National Natural Science Foundation of China (Grant No. 11501546)K.C.Wong Magna Fund in Ningbo University
文摘In this paper, we embed the integral form of the quantum supergroup U_v(gl_(m|n)) to the product of a family of integral quantum Schur super algebras. We show that the image of the embedding is a free Z[v, v^(-1)]-module by finding the basis explicitly and calculating the fundamental multiplication formulas of these bases. Unlike the non-super case, the fundamental multiplication formula, which is the key step, is more complicated since we have to deal with the case of multiplying the odd root vectors. As a consequence, via the base change, we realize the quantum supergroup at roots of unity as a subalgebra of the product of quantum Schur superalgebras. Thus, we find a new basis of quantum supergroups at odd roots of unity which comes from quantum Schur superalgebras.
