  Laumon moduli spaces are certain smooth closures of the moduli spaces of maps
from the projective line to the flag variety of GL_n. We construct the action
of the quantum loop algebra U_v(Lsl_n) in the equivariant K-theory of Laumon
spaces by certain natural correspondences. Also we construct the action of the
quantum toroidal algebra U^{tor}_v(Lsl}_n) in the equivariant K-theory of the
affine version of Laumon spaces. We write down explicit formulae for this
action in the affine Gelfand-Tsetlin base, corresponding to the fixed point
base in the localized equivariant K-theory.
