## Abstract

Given a reduced irreducible root system, the corresponding nil-DAHA is used to calculate the extremal coefficients of nonsymmetric Macdonald polynomials in the limit t→∞ and for antidominant weights, which is an important ingredient of the new theory of nonsymmetric q-Whittaker function. These coefficients are pure q-powers and their degrees are expected to coincide in the untwisted setting with the extremal degrees of the so-called PBW-filtration in the corresponding finite-dimensional irreducible representations of the simple Lie algebras for any root systems. This is a particular case of a general conjecture in terms of the level-one Demazure modules. We prove this coincidence for all Lie algebras of classical type and for G_{2}, and also establish the relations of our extremal degrees to minimal q-degrees of the extremal terms of the Kostant q-partition function; they coincide with the latter only for some root systems.

Original language | English |
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Pages (from-to) | 220-264 |

Number of pages | 45 |

Journal | Advances in Mathematics |

Volume | 282 |

DOIs | |

Publication status | Published - 10 Sep 2015 |

Externally published | Yes |

## Keywords

- Demazure modules
- Extremal weights
- Hecke algebras
- Kostant partition function
- Lie algebras
- Macdonald polynomials
- Root systems