Аннотация:
I will discuss how a family of Schur-Jack type polynomials naturally emerges as a representation space for infinite-dimensional quiver Yangian algebras. An initial example would be the affine Yangian of $\mathfrak{gl}_1$, in which the representation space is Jack polynomials (enumerated by Young diagrams) in time variables, and the generators of the algebra itself are generated by the cut-and-join operator. By analogy with the Cartan classification of Lie algebras, quiver Yangians are defined using a quiver and a superpotential. I will show how free-field representations of Fock-like representations are modified using the simplest examples, that is, how the set of “Young diagrams/time variables/Jack polynomials/cut-and-glue operator” generalizes for quivers beyond the $\mathfrak{gl}_1$ case.
