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- W2953079778 abstract "This paper is the continuation of the work in~cite{Yin}. 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~cite{KL, Lusztig1, Lusztig2}, which can be regarded as the special case $J=emptyset$. It also generalizes the work of Couillens~cite{C}, Deodhar~cite{Deodhar, Deodhar2}, and Douglass cite{MD}, corresponding to the parabolic cases." @default.
- W2953079778 created "2019-06-27" @default.
- W2953079778 creator A5011755709 @default.
- W2953079778 date "2015-03-31" @default.
- W2953079778 modified "2023-09-27" @default.
- W2953079778 title "W-graphs for Hecke algebras with unequal parameters(II)" @default.
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- W2953079778 doi "https://doi.org/10.48550/arxiv.1503.09081" @default.
- W2953079778 hasPublicationYear "2015" @default.
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