BMW algebras of simply laced type
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- October 2003
- DOI:
- 10.48550/arXiv.math/0310011
- arXiv:
- arXiv:math/0310011
- Bibcode:
- 2003math.....10011C
- Keywords:
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- Rings and Algebras;
- Group Theory;
- Representation Theory;
- 20F36 (Primary) 16G10;
- 16A40 (Secondary)
- E-Print:
- 39 pages