Representation theoretic realization of non-symmetric Macdonald polynomials at infinity

Evgeny Feigin, Syu Kato, Ievgen Makedonskyi

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

Abstract

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 {\mathrm{E}_{8}}.

Original languageEnglish
Pages (from-to)181-216
Number of pages36
JournalJournal fur die Reine und Angewandte Mathematik
Volume2020
Issue number764
DOIs
Publication statusPublished - 1 Jul 2020

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