Differential operator approach to $\imath$quantum groups and their oscillator representations
Quantum Algebra
2023-09-26 v2 Representation Theory
Abstract
For a quasi-split Satake diagram, we define a modified -Weyl algebra, and show that there is an algebra homomorphism between it and the corresponding quantum group. In other words, we provide a differential operator approach to quantum groups. Meanwhile, the oscillator representations of quantum groups are obtained. The crystal basis of the irreducible subrepresentations of these oscillator representations are constructed.
Cite
@article{arxiv.2203.03900,
title = {Differential operator approach to $\imath$quantum groups and their oscillator representations},
author = {Zhaobing Fan and Jicheng Geng and Shaolong Han},
journal= {arXiv preprint arXiv:2203.03900},
year = {2023}
}