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Israel Journal of Mathematics

, 173:335 | Cite as

Brauer algebras of simply laced type

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

Abstract

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.

Keywords

Irreducible Representation Positive Root Invariant Subspace Coxeter Group High Element 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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