Canonical bases for tensor products and super Kazhdan-Lusztig theory
Canonical bases for tensor products and super Kazhdan-Lusztig theory
复制标题
DOI：
10.1007/s00222-018-0801-5
复制
发表时间：
2018-08
影响因子：
0.8
通讯作者：
Huanchen Bao;Weiqiang Wang;Hideya Watanabe
中科院分区：
文献类型：
--
作者：
Huanchen Bao;Weiqiang Wang;Hideya Watanabe
本文发展了一个具有任意有限型参数的量子对称对的正则基的一般理论。我们构造了有限维单模及其张量积作为模的新的标准基。我们还构造了量子群的修正形式的正则基。为此，我们建立了几个新的量子对称对的结构结果，如双线性形式，辫子群作用，积分形式，Levi子代数（真实的秩1），和完整性的缠绕。
We develop a general theory of canonical bases for quantum symmetric pairswith parameters of arbitrary finite type. We construct new canonical bases for the finite-dimensional simple-modules and their tensor products regarded as-modules. We also construct a canonical basis for the modified form of thequantum group. To that end, we establish several new structural results on quantum symmetric pairs, such as bilinear forms, braid group actions, integral forms, Levi subalgebras (of real rank one), and integrality of the intertwiners.