Israel Journal of Mathematics

, 173:335 | Cite as

Brauer algebras of simply laced type

  • Arjeh M. CohenEmail author
  • Bart Frenk
  • David B. WalesEmail author


The diagram algebra introduced by Brauer that describes the centralizer algebra of the n-fold tensor product of the natural representation of an orthogonal Lie group has a presentation by generators and relations that only depends on the path graph A n − 1 on n − 1 nodes. Here we describe an algebra depending on an arbitrary graph Q, called the Brauer algebra of type Q, and study its structure in the cases where Q is a Coxeter graph of simply laced spherical type (so its connected components are of type A n − 1, D n , E6, E7, E8). We find its irreducible representations and its dimension, and show that the algebra is cellular. The algebra is generically semisimple and contains the group algebra of the Coxeter group of type Q as a subalgebra. It is a ring homomorphic image of the Birman-Murakami-Wenzl algebra of type Q; this fact will be used in later work determining the structure of the Birman-Murakami-Wenzl algebras of simply laced spherical type.


Irreducible Representation Positive Root Invariant Subspace Coxeter Group High Element 
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Copyright information

© Hebrew University Magnes Press 2009

Authors and Affiliations

  1. 1.Department of Mathematics and Computer ScienceTechnische Universiteit EindhovenEindhovenThe Netherlands
  2. 2.Mathematics DepartmentSloan Lab, CaltechPasadenaUSA

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