量子群及其振子表示的微分算子方法

IF 0.8 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2024-05-15 DOI:10.1007/s10114-024-2151-0

Zhao Bing Fan, Ji Cheng Geng, Shao Long Han

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引用次数: 0

摘要

对于准分裂 Satake 图，我们定义了一个修正的 q-Weyl 代数，并证明它与相应的 ı 量子群之间存在代数同构。换句话说，我们为 ı量子群提供了一种微分算子方法。同时，我们还得到了 ı量子群的振荡器表示。我们构建了这些振子表示的不可还原子表示的晶体基。

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Differential Operator Approach to ıquantum Groups and Their Oscillator Representations

For a quasi-split Satake diagram, we define a modified q-Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding ıquantum group. In other words, we provide a differential operator approach to ıquantum groups. Meanwhile, the oscillator representations of ıquantum groups are obtained. The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.