## 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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