The BLM realization for the integral form of U_v(gl_(m|n))

作     者：Xiaoyu Chen 

作者机构：Department of MathematicsNingbo University 

出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)

年 卷 期：2019年第62卷第2期

页      面：351-370页

核心收录：

学科分类：07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：supported by National Natural Science Foundation of China (Grant No. 11501546) K.C.Wong Magna Fund in Ningbo University 

主　　题：quantum supergroup quantum Schur superalgebra BLM basis integral form 

摘      要：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.