Macdonald polynomials, Laumon spaces and perverse coherent sheaves

Let G be an almost simple simply connected complex Lie group, and let G/U_- be its base affine space. In this paper we formulate a conjecture, which provides a new geometric interpretation of the Macdonald polynomials associated to G via perverse coherent sheaves on the scheme of formal arcs in the affinization of G/U_-. We prove our conjecture for G = SL(N) using the so called Laumon resolution of the space of quasi-maps (using this resolution one can reformulate the statement so that only “usual” (not perverse) coherent sheaves are used). In the course of the proof we also give a K-theoretic version of the main result of Negut (2009).