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arXiv · 1110.6214

A classification of commutative parabolic Hecke algebras

Peter Abramenko·James Parkinson·Hendrik Van Maldeghem
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Abstract

Let $(W,S)$ be a Coxeter system with $I\subseteq S$ such that the parabolic subgroup $W_I$ is finite. Associated to this data there is a \textit{Hecke algebra} $\scH$ and a \textit{parabolic Hecke algebra} $\scH^I=\mathbf{1}_I\scH\mathbf{1}_I$ (over a ring $\ZZ[q_s]_{s\in S}$). We give a complete classification of the commutative parabolic Hecke algebras across all Coxeter types.

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Peter Abramenko, James Parkinson, Hendrik Van Maldeghem. 2011-10-27. A classification of commutative parabolic Hecke algebras. https://arxiv.org/abs/1110.6214

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