Dipper-James-Murphy's conjecture for Hecke algebras of type B

2007/03/15 by Susumu Ariki, Ariki, Susumu, Nicolas Jacon +1 · 1 citation
Mathematics · #05E99 #17B37 #20C08 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Biology #Conjecture #Dipper #Ecology #FOS: Mathematics #History #Mathematics #Philosophy #Pure mathematics #Representation Theory (math.RT) #Type (biology) #math.RT #msc:05E99 #msc:17B37 #msc:20C08

paper · pdf · doi:10.48550/arxiv.math/0703447

published in arXiv (Cornell University) (Cornell University) · The revised version corrects minor points, the proof of lemma 3.3 has been improved

openalex publication_date 2007/03/15 · arxiv created 2007/12/11 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove a conjecture by Dipper, James and Murphy that a bipartition is restricted if and only if it is Kleshchev. Hence the restricted bipartitions naturally label the crystal graphs of level two irreducible integrable U_v(\mathfraksl_e)-modules and the simple modules of Hecke algebras of type B_n.

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