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A Construction of Representations of Loop Group and Affine Lie Algebra of \(\frak {sl}_{n}\)

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Abstract

We construct a family of representations of a central extension of loop group and affine Lie algebra for \(\frak {sl}_n\) and study their relations with highest weight modules. We also construct Whittaker functionals on our prepresentations.

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Authors and Affiliations

  1. Shanghai Center For Mathematical Sciences, Fudan University, Jiangwan Campus, 2005 Songhu Road, Shanghai, 200438, China

    Xuanzhong Dai

  2. Department of Mathematics, The Hong Kong University of Science and Technology, Clear Water Bay, Kowloon, Hong Kong

    Yongchang Zhu

Authors
  1. Xuanzhong Dai
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  2. Yongchang Zhu
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Correspondence to Yongchang Zhu.

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Presented by: Vyjayanthi Chari

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The second authorโ€™s research is supported by Hong Kong RGC grant 16305619.

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Dai, X., Zhu, Y. A Construction of Representations of Loop Group and Affine Lie Algebra of \(\frak {sl}_{n}\). Algebr Represent Theor 25, 649โ€“668 (2022). https://doi.org/10.1007/s10468-021-10039-9

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  • DOI: https://doi.org/10.1007/s10468-021-10039-9

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