高阶量子Serre关系  

Higher Order Quantum Serre Relations

作　　者：张立 ZHANG Li(College of Science,China Three Gorges University,Yichang 443002,China)

机构地区：[1]三峡大学理学院,湖北宜昌443002

出　　处：《数学的实践与认识》2024年第10期205-212,共8页Mathematics in Practice and Theory

摘　　要：Lusztig给出当整数N>M≥0,i=j+1时,有E_(i,i+1)^(N)E_(j,j+1)^(M)=∑_(0≤r≤M)(-1)^(r)[r+n-m-1n-m-1]E_(i,i+1)^(M-r)E_(j,j+1)^(M)E_(i,i+1)^(r+N-M)公式,这个公式被称为高阶量子Serre关系式.利用量子群的乘法公式和数学归纳法将这一结论进行推广,证明了这个公式当整数N>M≥0,|i-j|=1时也成立,它对研究整的量子群的生成元与关系式及其它类型代数的乘法公式有一定的帮助.Lusztig gives that when integer N>M≥O,i=j+1,there is a formula E_(i,i+1)^(N)E_(j,j+1)^(M)=∑_(0≤r≤M)(-1)^(r)[r+n-m-1n-m-1]E_(i,i+1)^(M-r)E_(j,j+1)^(M)E_(i,i+1)^(r+N-M),this formula is called the higher order quantum Serre relations.This article uses the multiplication formula of quantum groups and mathematical induction to generalize this conclusion,and proves that this formula also holds when N>M≥0,|i-j|=1,it is helpful for studying the generators and relationships of quantum groups of integers,as well as multiplication formulas of other types of algebras.

关 键 词：量子群 q-Schur代数 Serre关系 

分 类 号：O15[理学—数学]