Diffusion-limited erosion is a distinct universality class of fluctuating
interfaces. Although its dynamical exponent z=1, none of the known variants
of conformal invariance can act as its dynamical symmetry. In d=1 spatial
dimensions, its infinite-dimensional dynamic symmetry is constructed and shown
to be isomorphic to the direct sum of three loop-Virasoro algebras, with the
maximal finite-dimensional sub-algebra
sl(2,R)⊕sl(2,R)⊕sl(2,R).
The infinitesimal generators are spatially non-local and use the Riesz-Feller
fractional derivative. Co-variant two-time response functions are derived and
reproduce the exact solution of diffusion-limited erosion. The relationship
with the terrace-step-kind model of vicinal surfaces and the integrable XXZ
chain are discussed.Comment: Latex 2e, 28 pp, 4 figures (revised, with 2 new figures