TL;DR
This paper explores a specific class of W-graph ideals in Coxeter groups, linking them to Kazhdan-Lusztig left cells and supporting algorithms for constructing W-graphs for Specht modules in type A Hecke algebras.
Contribution
It identifies a new class of W-graph ideals that relate to Kazhdan-Lusztig cells, validating existing algorithms for W-graph construction in type A.
Findings
Identifies a class of W-graph ideals related to Kazhdan-Lusztig cells.
Provides theoretical justification for algorithms constructing W-graphs for Specht modules.
Links W-graph ideals to representation theory of Hecke algebras.
Abstract
In "W-graph ideals" (Robert B. Howlett and Van Minh Nguyen) the concept of a W-graph ideal in a Coxeter group was introduced, and it was shown how a W-graph can be constructed from a given W-graph ideal. In this paper, we describe a class of W-graph ideals from which certain Kazhdan-Lusztig left cells arise. The result justifies the algorithm as illustrated in "W-graph ideals" for the construction of W-graphs for Specht modules for the Hecke algebra of type A.
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Taxonomy
TopicsRings, Modules, and Algebras · Commutative Algebra and Its Applications