On Guay’s Evaluation Map for Affine Yangians

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Abstract

We give a detailed proof of the existence of evaluation map for affine Yangians of type A to clarify that it needs an assumption on parameters. This map was first found by Guay but a proof of its well-definedness and the assumption have not been written down in the literature. We also determine the highest weights of evaluation modules defined as the pull-back of integrable highest weight modules of the affine Lie algebra \(\hat {\mathfrak {gl}}_{N}\) by the evaluation map.

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  • 04 December 2020

    An Erratum to this paper has been published: <ExternalRef><RefSource>https://doi.org/10.1007/s10468-020-10011-z</RefSource><RefTarget Address="10.1007/s10468-020-10011-z" TargetType="DOI"/></ExternalRef>

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Number 17H06127 and 18K13390.

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Correspondence to Ryosuke Kodera.

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Presented by: Vyjayanthi Chari

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Kodera, R. On Guay’s Evaluation Map for Affine Yangians. Algebr Represent Theor 24, 253–267 (2021). https://doi.org/10.1007/s10468-019-09945-w

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Keywords

  • Affine Yangian
  • Evaluation map
  • Evaluation module

Mathematics Subject Classification (2010)

  • 17B10
  • 17B37
  • 17B67