2018/02/18 by Satoshi Naito, Naito, Satoshi, Daisuke Sagaki +1 · 1 citation
Mathematics · #14M15 #33D52 #81R10 #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Primary 17B37 #Quantum Algebra (math.QA) #Representation Theory (math.RT) #Secondary 14N15
paper · pdf · doi:10.48550/arxiv.1802.06339
openalex publication_date 2018/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let λ∈ P+ be a level-zero dominant integral weight, and w an arbitrary coset representative of minimal length for the cosets in W/Wλ, where Wλ is the stabilizer of λ in a finite Weyl group W. In this paper, we give a module \mathbbKw(λ) over the negative part of a quantum affine algebra whose graded character is identical to the specialization at t = ∞ of the nonsymmetric Macdonald polynomial Ew λ(q, t) multiplied by a certain explicit finite product of rational functions of q of the form (1 - q-r)-1 for a positive integer r. This module \mathbbKw(λ) (called a level-zero van der Kallen module) is defined to be the quotient module of the level-zero Demazure module Vw-(λ) by the sum of the submodules Vz-(λ) for all those coset representatives z of minimal length for the cosets in W/Wλ such that z > w in the Bruhat order