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Subrings of the asymptotic Hecke algebra of type \(H_4\). (English) Zbl 1196.20003

Summary: The structure of the subring \(J^{\Gamma\cap\Gamma^{-1}}\) of the asymptotic Hecke algebra is described for \(\Gamma\) a left cell of the Coxeter group of type \(H_4\). A small set of generators over \(\mathbb{Z}\) is produced. The subalgebras spanned by a subset of the basis \(\{t_x\}_{x\in\Gamma\cap\Gamma^{-1}}\) are determined.

MSC:

20C08 Hecke algebras and their representations
20F55 Reflection and Coxeter groups (group-theoretic aspects)
20C40 Computational methods (representations of groups) (MSC2010)
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