Resumen de Wreath Macdonald polynomials as eigenstates

Joshua Jeishing Wen

• We show that the wreath Macdonald polynomials forZ/Zn, when naturally viewed as elements in the vertex representation of the quantum toroidal algebra Uq,d( ¨ sl), diagonalize its horizontal Heisenberg subalgebra. Our proof makes heavy use of shuffle algebra methods, and we also obtain a new proof of existence of wreath Macdonald polynomials.