Imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$-modules in category $\mathcal O^q_{\text{red,im}}$

Ben Cox; Vyacheslav Futorny; Kailash C. Misra

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arXiv · 1812.02313

Imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$-modules in category $\mathcal O^q_{\text{red,im}}$

Ben Cox·Vyacheslav Futorny·Kailash C. Misra

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Abstract

Recently we defined imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$- modules in category $\mathcal O^q_{\text{red,im}}$ and showed the existence of such bases for reduced quantized imaginary Verma modules for $U_q(\widehat{\mathfrak{sl}(2)})$. In this paper we show the existence of imaginary crystal basis for any object in the category $\mathcal O^q_{\text{red,im}}$.

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Ben Cox, Vyacheslav Futorny, Kailash C. Misra. 2018-12-04. Imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$-modules in category $\mathcal O^q_{\text{red,im}}$. https://arxiv.org/abs/1812.02313

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