LLT polynomials in the Schiffmann algebra

We identify certain combinatorially defined rational functions which, under the shuffle to Schiffmann algebra isomorphism, map to LLT polynomials in any of the distinguished copies Lambda (X-m,X-n ) subset of E of the algebra of symmetric functions embedded in the elliptic Hall algebra E of Burban and Schiffmann. As a corollary, we deduce an explicit raising operator formula for the del operator applied to any LLT polynomial. In particular, we obtain a formula for backward difference del(m) s(lambda) which serves as a starting point for our proof of the Loehr-Warrington conjecture in a companion paper to this one.