Abstract
As is well known, the classical nonsingular Whittaker modules over quantum groups cannot be defined for non A1-type. In this paper, by choosing different generators for the quantum group \({U_q}({\mathfrak{g}\mathfrak{l}_{n + 1}})\), we introduce and study the twisted Whittaker modules over \({U_q}({\mathfrak{g}\mathfrak{l}_{n + 1}})\). We classify all the simple twisted Whittaker modules with nonsingular Whittaker functions. This agrees Kostant’s results on Whittaker modules for the simple complex Lie algebras \({\mathfrak{s}\mathfrak{l}_{n + 1}}\) as q approaches 1.
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Acknowledgements
This work was supported by National Natural Science Foundation of China (Grant Nos. 11871249, 11871190 and 12171155) and Natural Sciences and Engineering Research Council of Canada (Grant No. 311907-2015). The authors thank the referees for their nice suggestions.
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Xia, L., Zhao, K. Twisted Whittaker modules over \({U_q}({\mathfrak{g}\mathfrak{l}_{n + 1}})\). Sci. China Math. 66, 2191–2202 (2023). https://doi.org/10.1007/s11425-022-2079-3
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DOI: https://doi.org/10.1007/s11425-022-2079-3