由量子对称对产生的正则基
Canonical bases arising from quantum symmetric pairs
摘要：
我们发展了一个一般性的正则基理论，给出了参数为任意有限型的量子对称对$(\mathbf{U}, \mathbf{U}^\imath)$的正则基。我们构造了简单可积$\mathbf{U}$ -模及其张量积作为$\mathbf{U}^\imath$ -模的新的标准基.我们还构造了$\imath$量子群$\mathbf{U}^\imath$的修正形式的正则基。为此，我们建立了量子对称对的几个新的结构结果，如双线性型，辫群作用，积分形式，Levi子代数（实秩1），和intertwiners的完整性。
英文摘要：
We develop a general theory of canonical bases for quantum symmetric pairs $(\mathbf{U}, \mathbf{U}^\imath)$ with parameters of arbitrary finite type. We construct new canonical bases for the simple integrable $\mathbf{U}$-modules and their tensor products regarded as $\mathbf{U}^\imath$-modules. We also construct a canonical basis for the modified form of the $\imath$quantum group $\mathbf{U}^\imath$. 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.
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