Title: Representation theoretic realization of non-symmetric Macdonald polynomials at infinity,
Abstract: We study the nonsymmetric Macdonald polynomials specialized at infinity from
various points of view. First, we define a family of modules of the Iwahori
algebra whose characters are equal to the nonsymmetric Macdonald polynomials
specialized at infinity. Second, we show that these modules are isomorphic to
the dual spaces of sections of certain sheaves on the semi-infinite Schubert
varieties. Third, we prove that the global versions of these modules are
homologically dual to the level one affine Demazure modules.