  We define monotone links on a torus, obtained as projections of curves in the
plane whose coordinates are monotone increasing. Using the work of
Morton-Samuelson, to each monotone link we associate elements in the double
affine Hecke algebra and the elliptic Hall algebra. In the case of torus knots
(when the curve is a straight line), we recover symmetric function operators
appearing in the rational shuffle conjecture.
  We show that the class of monotone links viewed as links in $\mathbb R^3$
coincides with the class of Coxeter links, studied by Oblomkov-Rozansky in the
setting of the flag Hilbert scheme. When the curve satisfies a convexity
condition, we recover positroid links that we previously studied. In the convex
case, we conjecture that the associated symmetric functions are Schur positive,
extending a recent conjecture of Blasiak-Haiman-Morse-Pun-Seelinger, and we
speculate on the relation to Khovanov-Rozansky homology.
  Our constructions satisfy a skein recurrence where the base case consists of
piecewise almost linear curves. We show that convex piecewise almost linear
curves give rise to algebraic links.
