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arXiv · 1707.05563

On the presentation of Hecke-Hopf algebras for non-simply-laced type

Weideng Cui
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Abstract

Hecke-Hopf algebras were defined by A. Berenstein and D. Kazhdan. We give an explicit presentation of an Hecke-Hopf algebra when the parameter $m_{ij},$ associated to any two distinct vertices $i$ and $j$ in the presentation of a Coxeter group, equals $4,$ $5$ or $6$. As an application, we give a proof of a conjecture of Berenstein and Kazhdan when the Coxeter group is crystallographic and non-simply-laced. As another application, we show that another conjecture of Berenstein and Kazhdan holds when $m_{ij},$ associated to any two distinct vertices $i$ and $j,$ equals $4$ and that the conjecture does not hold when some $m_{ij}$ equals $6$ by giving a counterexample to it.

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Weideng Cui. 2017-07-20. On the presentation of Hecke-Hopf algebras for non-simply-laced type. https://arxiv.org/abs/1707.05563

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