TL;DR
This paper introduces the concept of W-graph ideals in Coxeter groups and provides a method to construct W-graphs from these ideals, with applications to Specht modules in type A.
Contribution
It defines W-graph ideals and presents an algorithm to construct W-graphs from them, advancing the understanding of their structure and applications.
Findings
Provides a construction method for W-graphs from W-graph ideals
Applies the construction to Specht modules in type A
Enhances the combinatorial understanding of Coxeter groups
Abstract
We introduce a concept of a W-graph ideal in a Coxeter group. The main goal of this paper is to describe how to construct a W-graph from a given W-graph ideal. The principal application of this idea is in type A, where it provides an algorithm for the construction of W-graphs for Specht modules.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry