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29 March 2024
 
  » arxiv » math.RA/0310011

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BMW algebras of simply laced type
A. M. Cohen ; D. A. H. Gijsbers ; D. B. Wales ;
Date 1 Oct 2003
Subject Rings and Algebras; Group Theory; Representation Theory MSC-class: 20F36 (Primary) 16G10, 16A40 (Secondary) | math.RA math.GR math.RT
AbstractIt 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.
Source arXiv, math.RA/0310011
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