2007/04/20 by Arjeh M Cohen, Arjeh M. Cohen, Cohen, Arjeh M +5
Mathematics · #16K20 #17Bxx #20F36 #20Fxx #20M05 #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #math.GR #math.RT #msc:16K20 #msc:17Bxx #msc:20F36 #msc:20Fxx #msc:20M05
paper · pdf · doi:10.48550/arxiv.0704.2732
19 pages
openalex publication_date 2007/04/20 · arxiv created 2007/04/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The diagram algebra introduced by Brauer that describes the centralizer algebra on tensor products of the natural representation of an orthogonal group has a presentation by generators and relations that only depends on the graph of type An on n nodes. Here we describe an algebra depending on an arbitrary graph of type M. We study its structure when the type is An, Dn, E6, E7, E8. We determine the representations and find the dimensions. The algebra is generically semisimple and contains the group algebra of the Coxeter type M as a subalgebra. It is a ring homomorphism of the Birman-Murakami-Wenzl algebra of these types. This fact will be used in later work determining the structure of Birman-Murakami-Wenzl algebras of simply laced spherical type.