Hecke Algebras in Algebra and Analysis

本程序的目的是采用调和分析和算子-代数表示理论中的技术来研究在代数和几何环境中产生的Hecke代数。相关的解析结构是C*-代数，那么基本问题是“哪些Hecke代数有忠实的包络C*-代数？”我们首先发展了一个适当的半群交叉积理论，然后利用拓扑化的概念研究了Hecke代数，这使得我们能够在拓扑群的背景下研究Hecke代数。

The aim of this program is to adapt techniques from harmonic analysis and operator-algebraic representation theory to study Hecke algebras arising in algebraic and geometric settings. The relevant analytic structures are C*-algebras and the fundamental question is then "Which Hecke algebras have a faithful enveloping C*-algebra?" We investigate this question, first by developing an appropriate theory of crossed products by semigroups and, second, by using the notion of topologization which enables the Hecke algebra to be studied in the context of topological groups.