Vertex representations for Yangians of Kac-Moody algebras

Nicolas Guay; Vidas Regelskis; Curtis Wendlandt

doi:10.5802/jep.103

Vertex representations for Yangians of Kac-Moody algebras
[Représentations vertex pour les Yangiens d’algèbres de Kac-Moody]

Nicolas Guay ¹ ; Vidas Regelskis ^2,³ ; Curtis Wendlandt ¹

¹ University of Alberta, Department of Mathematical and Statistical Sciences Edmonton, AB T6G 2G1, Canada
² University of York, Department of Mathematics York, YO10 5DD, UK
³ Vilnius University, Institute of Theoretical Physics and Astronomy Saulėtekio av. 3, Vilnius 10257, Lithuania

Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 665-706.

Résumé
Abstract

À l’aide d’opérateurs vertex, nous construisons des représentations du Yangien d’une algèbre de Kac-Moody simplement lacée et de son double. Comme corollaire, nous démontrons la propriété de Poincaré-Birkhoff-Witt pour les Yangiens affines simplement lacés.

Using vertex operators, we build representations of the Yangian of a simply laced Kac-Moody algebra and of its double. As a corollary, we prove the Poincaré-Birkhoff-Witt property for simply laced affine Yangians.

Reçu le : 2018-04-24
Accepté le : 2019-07-25
Publié le : 2019-09-24

Zbl

DOI : 10.5802/jep.103

Classification : 17B37, 81R10, 17B69
Keywords: Yangian, vertex operator, Kac-Moody algebra, Fock space, twisted group algebra, central extension
Mot clés : Yangien, opérateur vertex, algèbre de Kac-Moody, espace de Fock, algèbre de groupe tordue, extension centrale

Affiliations des auteurs :

Nicolas Guay ¹ ; Vidas Regelskis ^{2, 3} ; Curtis Wendlandt ¹

¹ University of Alberta, Department of Mathematical and Statistical Sciences Edmonton, AB T6G 2G1, Canada
² University of York, Department of Mathematics York, YO10 5DD, UK
³ Vilnius University, Institute of Theoretical Physics and Astronomy Saulėtekio av. 3, Vilnius 10257, Lithuania

Licence :

CC-BY 4.0

Droits d'auteur : Les auteurs conservent leurs droits

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     author = {Nicolas Guay and Vidas Regelskis and Curtis Wendlandt},
     title = {Vertex representations for {Yangians} of {Kac-Moody} algebras},
     journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques},
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Nicolas Guay; Vidas Regelskis; Curtis Wendlandt. Vertex representations for Yangians of Kac-Moody algebras. Journal de l’École polytechnique — Mathématiques, Tome 6 (2019), pp. 665-706. doi : 10.5802/jep.103. https://jep.centre-mersenne.org/articles/10.5802/jep.103/

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