Vertex Representations for Yangians of Kac-Moody algebras

Abstract

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 PBW property for simply laced affine Yangians.

arXiv comment30 pages

References in corpus (12)

• Coproduct for the Yangian of an affine Kac-Moody algebra
• On the R-matrix realization of Yangians and their representations
• Yangians and quantum loop algebras
• Equivalences between three presentations of orthogonal and symplectic Yangians
• A level-one representation of the quantum affine superalgebra $\U_q(\hat{\frak{sl}}(M+1|N+1))$
• Shifted quantum affine algebras: integral forms in type $A$ (with appendices by Alexander Tsymbaliuk and Alex Weekes)
• A central extension of $\cD Y_{\hbar}(\gtgl_2)$ and its vertex representations
• Homomorphisms between different quantum toroidal and affine Yangian algebras
• Yangians, quantum loop algebras and abelian difference equations
• Quantum Z-algebras and representations of quantum affine algebras
• Cohomological Hall algebras and affine quantum groups
• An explicit isomorphism between quantum and classical sl(n)

Cited by in corpus (8)

• On Guay's evaluation map for affine Yangians
• Coproduct for affine Yangians and parabolic induction for rectangular $W$-algebras
• Yangian doubles of classical types and their vertex representations
• The formal shift operator on the Yangian double
• Level one Weyl modules for toroidal Lie algebras
• The restricted quantum double of the Yangian
• The R-matrix presentation for the rational form of a quantized enveloping algebra
• Quiver Yangian algebras associated to Dynkin diagrams of A-type and their rectangular representations