Gluing affine Yangians with bi-fundamentals

• Published in: The journal of high energy physics Vol. 2020; no. 6; pp. 182 - 64
• Main Author: Li, Wei
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.06.2020; Springer Nature B.V; SpringerOpen
• Subjects: Algebra; Classical and Quantum Gravitation; Conformal and W Symmetry; Construction; Elementary Particles; Gluing; High energy physics; Higher Spin Symmetry; Integrable Hierarchies; Mathematical analysis; Operators (mathematics); Parameters; Physics; Physics and Astronomy; Quantum Field Theories; Quantum Field Theory; Quantum Physics; Regular Article - Theoretical Physics; Relativity Theory; String Theory; Symmetry; Integrable Hierarchies; Conformal and W Symmetry; Higher Spin Symmetry
• ISSN: 1029-8479; 1029-8479
• DOI: 10.1007/JHEP06(2020)182

A bstract The affine Yangian of gl 1 is isomorphic to the universal enveloping algebra of W 1 + ∞ and can serve as a building block in the construction of new vertex operator algebras. In [1], a two-parameter family generalization of N = 2 supersymmetric W ∞ algebra was constructed by “gluing” two affine Yangians of gl 1 using operators that transform as (□, □ ¯ ) and ( □ ¯ , □) w.r.t. the two affine Yangians. In this paper we realize a similar (but non-isomorphic) two-parameter gluing construction where the gluing operators transform as (□, □) and ( □ ¯ , □ ¯ ) w.r.t. the two affine Yangians. The corresponding representation space consists of pairs of plane partitions connected by a common leg whose cross-section takes the shape of Young diagrams, offering a more transparent geometric picture than the previous construction.