On Guay’s Evaluation Map for Affine Yangians

  • Ryosuke KoderaEmail author


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.


Affine Yangian Evaluation map Evaluation module 

Mathematics Subject Classification (2010)

17B10 17B37 17B67 


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


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© Springer Nature B.V. 2020

Authors and Affiliations

  1. 1.Department of Mathematics, Graduate School of ScienceKobe UniversityKobeJapan

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