$q$-Analogue of the degree zero part of a rational Cherednik algebra and generalised Van Diejen's Hamiltonians

Misha Feigin, Martin Vrabec

Inside the double affine Hecke algebra of type $G{L}_n$, which depends on two parameters $q$ and $\tau$, we define a subalgebra ${\mathbb{H}}^{{\mathfrak{gl}}_n}$ that may be thought of as…