• A
  • A
  • A
  • ABC
  • ABC
  • ABC
  • А
  • А
  • А
  • А
  • А
Regular version of the site

Article

Representation theoretic realization of non-symmetric Macdonald polynomials at infinity

Journal fuer die reine und angewandte Mathematik. 2020. Vol. 764. P. 181-216.
Feigin E., Kato S., Makedonskyi I.

We study the non-symmetric 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 non-symmetric 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 for simply-laced Dynkin types except for type $E_8$