2015/03/31 by Yunchuan Yin, Yin, Yunchuan
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.1503.09081
openalex publication_date 2015/03/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is the continuation of the work in~\citeYin. In that paper we generalized the definition of W-graph ideal in the weighted Coxeter groups, and showed how to construct a W-graph from a given W-graph ideal in the case of unequal parameters. In this paper we study the full W-graphs for a given W-graph ideal. We show that there exist a pair of dual modules associated with a given W-graph ideal, they are connected by a duality map. % and the dual W-graph bases can be established. For each of the dual modules, the associated full W-graphs can be constructed.% among them, another pair of dual bases are obtained by using %the inversions of the relative Kazhdan-Lusztig polynomials. Our construction closely parallels that of Kazhdan and Lusztig~\citeKL, Lusztig1, Lusztig2, which can be regarded as the special case J=∅. It also generalizes the work of Couillens~\citeC, Deodhar~\citeDeodhar, Deodhar2, and Douglass \citeMD, corresponding to the parabolic cases.