2007/04/16 by Meinolf Geck, Geck, Meinolf, Lacrimioara Iancu +4
Mathematics · #20C08 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Representation Theory (math.RT) #math.RT #msc:20C08
paper · pdf · doi:10.48550/arxiv.0704.1846
the revised version corrects some minor errors
openalex publication_date 2007/04/16 · arxiv created 2007/06/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Dipper, James and Murphy generalized the classical Specht module theory to Hecke algebras of type Bn. On the other hand, for any choice of a monomial order on the parameters in type Bn, we obtain corresponding Kazhdan--Lusztig cell modules. In this paper, we show that the Specht modules are naturally equivalent to the Kazhdan--Lusztig cell modules \em if we choose the dominance order on the parameters, as in the ``asymptotic case'' studied by Bonnafé and the second named author. We also give examples which show that such an equivalence does not hold for other choices of monomial orders.