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arXiv · 2203.03900

Differential operator approach to $\imath$quantum groups and their oscillator representations

Zhaobing Fan·Jicheng Geng·Shaolong Han
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Abstract

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 $\imath$quantum group. In other words, we provide a differential operator approach to $\imath$quantum groups. Meanwhile, the oscillator representations of $\imath$quantum groups are obtained. The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.

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Zhaobing Fan, Jicheng Geng, Shaolong Han. 2022-03-08. Differential operator approach to $\imath$quantum groups and their oscillator representations. https://arxiv.org/abs/2203.03900

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