2008/10/17 by Claire Levaillant, Claire Isabelle Levaillant, Levaillant, Claire Isabelle
Mathematics · #16G32 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:16G32
paper · pdf · doi:10.48550/arxiv.0810.3205
8 pages
openalex publication_date 2008/10/17 · arxiv created 2008/10/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is known that the Lawrence-Krammer representation of the Artin group of type An-1 based on the two parameters t and q that was used by Krammer and independently by Bigelow to show the linearity of the braid group on n strands is generically irreducible. Here, we recover this result and show further that for some complex specializations of the parameters the representation is reducible. We give all the values of the parameters for which the representation is reducible as well as the dimensions of the invariant subspaces. We deduce some results of semisimplicity of the Birman-Murakami-Wenzl algebra of type An-1.