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Abstract: The diagram algebra introduced by Brauer that describes the centralizeralgebra on tensor products of the natural representation of an orthogonal grouphas a presentation by generators and relations that only depends on the graphof type An on n nodes. Here we describe an algebra depending on an arbitrarygraph of type M. We study its structure when the type is An, Dn, E6, E7, E8. Wedetermine the representations and find the dimensions. The algebra isgenerically semisimple and contains the group algebra of the Coxeter type M asa subalgebra. It is a ring homomorphism of the Birman-Murakami-Wenzl algebra ofthese types. This fact will be used in later work determining the structure ofBirman-Murakami-Wenzl algebras of simply laced spherical type.

Autor: Arjeh M Cohen, Bart Frenk, David Wales


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