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BMW algebras of simply laced type

Cohen, Arjeh M. and Gijsbers, Dié A. H. and Wales, David B. (2003) BMW algebras of simply laced type. . (Unpublished)

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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.

Item Type:Report or Paper (Discussion Paper)
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Record Number:CaltechAUTHORS:20191009-091742763
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:99179
Deposited By: Tony Diaz
Deposited On:09 Oct 2019 17:48
Last Modified:09 Oct 2019 17:48

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