Hecke Algebras in Algebra and Analysis

本课程的目的是将调和分析和算子代数表示理论的技术应用于代数和几何环境下的赫克代数研究。相关的解析结构是C*-代数，那么最基本的问题是“哪个赫克代数有一个可靠的包络C*-代数？”我们研究这个问题，首先通过发展半群交叉积的适当理论，其次，通过使用拓扑化的概念，使Hecke代数能够在拓扑群的背景下进行研究。

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.