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A type B analog of the Lie representation

Abstract : 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 Sn−1, 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 Bn−1. 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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  • HAL Id : hal-02173742, version 1

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Andrew Berget. A type B analog of the Lie representation. 28-th International Conference on Formal Power Series and Algebraic Combinatorics, Simon Fraser University, Jul 2016, Vancouver, Canada. ⟨hal-02173742⟩

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