The Integral Quantum Loop Algebra of gl(n)
The Integral Quantum Loop Algebra of gl(n)
复制标题
gl(n) 的积分量子环代数
DOI：
10.1093/imrn/rnx300
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发表时间：
2019
影响因子：
1
通讯作者：
Fu Qiang
中科院分区：
文献类型：
--
作者：
Du Jie;Fu Qiang
我们将通过证明猜想[，3.8.6]构造的量子圈代数的Lusztig形式，并在这种情况下部分地建立积分水平上的Schur-Weyl对偶。我们还将调查的积分形式的修改量子仿射通过引入一个仿射稳定的属性，并将提升规范基地从仿射量子舒尔代数的规范基础，这个积分形式。作为我们理论的应用，我们还将讨论修改的扩展量子仿射的积分形式并构造其典范基，以提供与Lusztig在[，§9.3]中的猜想相关的替代代数结构，该猜想已在中得到证明。
We will construct the Lusztig form for the quantum loop algebra ofby proving the conjecture [, 3.8.6] and establish partially the Schur–Weyl duality at the integral level in this case. We will also investigate the integral form of the modified quantum affineby introducing an affine stabilisation property and will lift the canonical bases from affine quantum Schur algebras to a canonical basis for this integral form. As an application of our theory, we will also discuss the integral form of the modified extended quantum affineand construct its canonical basis to provide an alternative algebra structure related to a conjecture of Lusztig in [, §9.3], which has been already proved in .