Quantum affine Gelfand-Tsetlin bases and quantum toroidal algebra via K-theory of affine Laumon spaces

摘要

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