# Representation theoretic realization of non-symmetric Macdonald polynomials at infinity

## TL;DR

This paper provides a representation-theoretic framework for nonsymmetric Macdonald polynomials at infinity, linking algebraic modules, geometric sheaves, and duality in affine Lie algebra representations.

## Contribution

It introduces modules of the Iwahori algebra whose characters match these specialized polynomials and establishes their geometric and duality properties.

## Key findings

- Modules are isomorphic to dual spaces of sheaf sections on semi-infinite Schubert varieties
- Global modules are homologically dual to level one affine Demazure modules
- Characters of modules equal nonsymmetric 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.