Abstract
In this paper, we first prove that the affine Yangian of gl̂(1) is isomorphic to the algebra YB0gl̂(1) whose generators ej, fj, ψj are defined using the Maulik–Okounkov R-matrix. Then, we provide the MacMahon representation of YBgl̂(1) which is generated by hj, ej, fj, ψj and find that the representation in the zero twist integrable system is isomorphic to the MacMahon representation. Finally, we discuss a special case in the zero twist integrable system, we obtain one kind of symmetric functions Yλ(p⃗) defined on two-dimensional Young diagrams, which are symmetric about the x-axis and y-axis, and the symmetric functions Yλ(p⃗) become Jack polynomials and Schur functions in special cases.
Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
