The BLM realization for the integral form of Uv(g(l)m丨n)

• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2019,（2）
• 页码范围: 351-370
• 页数: 20页
• 语种: 英文

摘要

In this paper,we embed the integral form of the quantum supergroup Uv(g(l)m丨n) to the product of a family of integral quantum Schur superalgebras.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.