Representations of the Double Dyck Path Algebra and Connections to the Elliptic Hall Algebra

The double Dyck path algebra B_{q,t} is constructed from an infinite quiver of affine Hecke algebras connected via raising and lowering operators. In this talk I will discuss joint work with Eugene Gorsky and Jose Simental where we construct and classify the semisimple representations of  B_{q,t}. I will also explain how the elliptic Hall algebra arises as the spherical subalgebra of B_{q,t}.