W-graph ideals and biideals

2015/03/02 by Robert B. Howlett, Howlett, Robert B., Van Minh Nguyen +1
Mathematics · #20C08 #20C30 #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings, Modules, and Algebras #math.GR #math.RT #msc:20C08 #msc:20C30

paper · pdf · doi:10.48550/arxiv.1503.00408

32 pages

openalex publication_date 2015/03/02 · arxiv created 2015/03/04 · arxiv updated 2015/03/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We further develop the theory of W -graph ideals, first introduced by the authors in reference [6]. We discuss W -graph subideals, and induction and restriction of W -graph ideals for parabolic subgroups. We introduce W -graph biideals: those W -graph ideals that yield (W× W^{\mathrm o})-graphs, where W^{\mathrm o} is the group opposite to W. We determine all W -graph ideals and biideals in finite Coxeter groups of rank 2.

Related

• W-graph ideals
• W-graph ideals II
• W-graphs for Hecke algebras with unequal parameters(II)
• A Reduction theorem for the W-graph decomposition conjecture
• An extension of a theorem and errata for "A Class of Representations of\n Hecke Algebras"