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In Sect. 21.1 we define the Hecke algebra \({\mathbb R}_{\mathbf q} W\) associated to a Coxeter system \((W,S)\) and a certain tuple of numbers \({\mathbf q}\) . It is a deformation of the group algebra \({\mathbb R} W\) . Hecke algebras arise in the study of buildings of type \((W,S)\) with thickness vector \({\mathbf q}\) .

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Hecke–von Neumann Algebras

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  • 发表日期：

    2025年

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  • Michael W. Davis

摘要

In Sect. 21.1 we define the Hecke algebra \({\mathbb R}_{\mathbf q} W\) associated to a Coxeter system \((W,S)\) and a certain tuple of numbers \({\mathbf q}\) . It is a deformation of the group algebra \({\mathbb R} W\) . Hecke algebras arise in the study of buildings of type \((W,S)\) with thickness vector \({\mathbf q}\) .