Extremal part of the PBW-filtration and nonsymmetric Macdonald polynomials

Ivan Cherednik, Evgeny Feigin

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)

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 G2, 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 languageEnglish
Pages (from-to)220-264
Number of pages45
JournalAdvances in Mathematics
Volume282
DOIs
Publication statusPublished - 10 Sep 2015
Externally publishedYes

Keywords

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

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