Brauer algebras of simply laced type
- Creators
- Cohen, Arjeh M.
- Frenk, Bart
- Wales, David B.
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 , E_6, E_7, E_8). 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.
Additional Information
© Hebrew University Magnes Press 2009. Received: 9 May 2007. Revised: 30 January 2008. Published online: 4 December 2009.Additional details
- Eprint ID
- 17093
- Resolver ID
- CaltechAUTHORS:20100107-113013608
- Created
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2010-01-12Created from EPrint's datestamp field
- Updated
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2023-06-01Created from EPrint's last_modified field