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

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

Representation Theory 2018-12-07 v1

Authors: Ben Cox , Vyacheslav Futorny , Kailash C. Misra

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 $\mathcal O^q_{\text{red,im}}$ .

Keywords

imaginary crystal bases quantum affine algebra category o reduced quantized verma modules uq(sl(2))

Cite

@article{arxiv.1812.02313,
  title  = {Imaginary crystal bases for $U_q(\widehat{\mathfrak{sl}(2)})$-modules in category $\mathcal O^q_{\text{red,im}}$},
  author = {Ben Cox and Vyacheslav Futorny and Kailash C. Misra},
  journal= {arXiv preprint arXiv:1812.02313},
  year   = {2018}
}

Comments

13 pages. arXiv admin note: text overlap with arXiv:1509.00865, arXiv:0903.1062

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

Abstract

Keywords

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