Proceedings of the 28-th International Conference on Formal Power Series and Algebraic Combinatorics
4-8 Jul 2016 Vancouver, British Columbia (Canada)
A type B analog of the Lie representation
Andrew Berget  1  
1 : Department of Mathematics [Bellingham]  -  Website
Western Washington University 516 High Street - MS-9063 Bellingham -  États-Unis

We describe a type B analog of the much studied Lie representation of the symmetric group. The nth Lie representation of Sn restricts to the regular representation of Sn1, and our generalization mimics this property. Specifically, we construct a representation of the type B Weyl group Bn that restricts to the regular representation of Bn1. We view both of these representations as coming from the internal zonotopal algebra of the Gale dual of the corresponding reflection arrangements. 

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