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Representation Theory

Published by the American Mathematical Society since 1997, this electronic-only journal is devoted to research in representation theory and seeks to maintain a high standard for exposition as well as for mathematical content. All articles are freely available to all readers and with no publishing fees for authors.

ISSN 1088-4165

The 2020 MCQ for Representation Theory is 0.71.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Realizations of $A_1^{(1)}$-modules in category $\widetilde {\mathcal O}$
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by Fulin Chen, Yun Gao and Shaobin Tan;
Represent. Theory 27 (2023), 149-176
DOI: https://doi.org/10.1090/ert/632
Published electronically: May 11, 2023

Abstract:

In this paper, we give an explicit realization of all irreducible modules in Chari’s category $\widetilde {\mathcal O}$ for the affine Kac-Moody algebra $A_{1}^{(1)}$ by using the idea of free fields. We work on a much more general setting which also gives us explicit realizations of all simple weight modules for certain current algebra of $\mathfrak {sl}_2(\mathbb {C})$ with finite weight multiplicities, including the polynomial current algebra $\mathfrak {sl}_2(\mathbb {C})\otimes \mathbb {C}[t]$, the loop algebra $\mathfrak {sl}_2(\mathbb {C})\otimes \mathbb {C}[t,t^{-1}]$ and the three-point Lie algebra $\mathfrak {sl}_2(\mathbb {C})\otimes \mathbb {C}[t,t^{-1},(t-1)^{-1}]$ arisen in the work by Kazhdan-Lusztig.
References
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Bibliographic Information
  • Fulin Chen
  • Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen 361005, People’s Republic of China
  • MR Author ID: 936518
  • Email: chenf@xmu.edu.cn
  • Yun Gao
  • Affiliation: Department of Mathematics and Statistics, York University, Toronto M3J 1P3, Canada
  • Email: ygao@yorku.ca
  • Shaobin Tan
  • Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen 361005, People’s Republic of China
  • Email: tans@xmu.edu.cn
  • Received by editor(s): July 19, 2021
  • Received by editor(s) in revised form: September 27, 2022
  • Published electronically: May 11, 2023
  • Additional Notes: The first author was partially supported by China NSF grant (Nos. 11971397, 12161141001). The second author was partially supported by NSERC of Canada and NSFC grant 11931009. The third author was partially supported by China NSF grant (No. 12131018)
  • © Copyright 2023 American Mathematical Society
  • Journal: Represent. Theory 27 (2023), 149-176
  • MSC (2020): Primary 17B67
  • DOI: https://doi.org/10.1090/ert/632
  • MathSciNet review: 4587549