BMW algebras of simply laced type

BMW algebras of simply laced type

It is known that the recently discovered representations of the Artin groups of type A_n, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type D_n and E_n which also lead to the newly found faithful representations of the Artin groups of the corresponding type...

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Hauptverfasser: Cohen, A. M, Gijsbers, D. A. H, Wales, D. B
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Mathematics - Group Theory
Mathematics - Representation Theory
Mathematics - Rings and Algebras
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Gijsbers, D. A. H
Wales, D. B
description It is known that the recently discovered representations of the Artin groups of type A_n, the braid groups, can be constructed via BMW algebras. We introduce similar algebras of type D_n and E_n which also lead to the newly found faithful representations of the Artin groups of the corresponding types. We establish finite dimensionality of these algebras. Moreover, they have ideals I_1 and I_2 with I_2 contained in I_1 such that the quotient with respect to I_1 is the Hecke algebra and I_1/I_2 is a module for the corresponding Artin group generalizing the Lawrence-Krammer representation. Finally we give conjectures on the structure, the dimension and parabolic subalgebras of the BMW algebra, as well as on a generalization of deformations to Brauer algebras for simply laced spherical type other than A_n.
doi_str_mv 10.48550/arxiv.math/0310011
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Mathematics - Representation Theory
Mathematics - Rings and Algebras
title BMW algebras of simply laced type
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